Most probably the species will have a name for the light consisting of all wavelengths they can perceive, all of them fully saturated. This, respective to our standards is something we call white. For them the Sun will be just as "white" as it is for us and their star will be for us as white as the Sun is.
Atmosphere can significantly impact colours. We can perceive the colour of star at their ground level as violet while they can perceive ours as "orange" (in their terms). It may even happen that stars will be totally invisible for them on our planet and for us on theirs even though both we can see them on Earth and they will see it on their planet.
It is also possible, that they will use that very same name for the electromagnetic pulse saturated in full spectrum of electromagnetic wavelength of some range just like we do, but they may as well have some totally different name for it.
It's all just not so simple.
How we see
To understand why we see colours we need to understand how is it possible that we actually "see". There are 3 layers responsible for that:
- Physics (what reaches our eyes)
- Physiology (how the light is converted into neural signals)
- Psychology (how our brain interprets the signals that reach it)
Let's go one by one.
What we call light is actually an electromagnetic pulse in a certain range of wavelengths that (depending on the accuracy of definition) either humans are in general capable of perceiving through their sense of vision (a more common term) or physicians have defined as light (a scientific definition). The term light as we usually use it is the first one and all of this "light" is included in the second one (with plenty of additions).
Whenever we look at an object, what we actually see depends on the electromagnetic pulse that comes from the direction of that object (and can consist of pulse produced by the object, reflected by the object and that went through the object). I will get back to that later.
The Sun and pretty much all stars emit electromagnetic pulses that consists of the wide spectrum of wavelengths, from IR (or even radio) to X-Rays and Gamma. There are some (very small) bits missing and some of them are stronger than others but all in all you can "see" Sun if you look in "visible" light, UV, IR and other frequencies.
These are photos of the Sun taken in various frequencies (taken from this page).
For comparison, this are the spectres of other stars (as observed on the Earth - remember about the Doppler effect that shifts the frequencies, taken from space.fm)
As you can see, most wavelengths are covered which essentially means - those stars are to our eyes white.
Essentially humans see through their eyes. To be more specific - those are the organs that capture light, focus it and change it into the electric signals that can be transmitted through a nerve system to a brain. Let me focus on that last role of eyes. Retina of a human eye is covered with two main types of light receptors - cones and rodes. Cones are further split into three subtypes. Each of those types responds to a different range of an electromagnetic wavelength (and within the range where it reacts the strength of reaction is different).
Here is a representation how human rods and cones are sensitive to specific wavelengths (from this page):
Let me add that rods and cones cannot work at the same time. There is a simple mechanism that "turns on and off" rods when respectively there is not enough or sufficiently enough light for cones to operate. Let me just focus on cones as they are responsible for our colourful vision. When a specific area of an eye is exposed to some visible light (in common understanding - visible to us), the cones of that eye are "activated" if this light consists electromagnetic within specific wavelength. As a result it send impulses to brain. A strength of such depends on strength of the light of this wavelength and how close the wavelength is to the peak of the sensitivity are wavelength. If we look at something green, yellow and orange, in each case both M cone and L cone will be activated, but with each of the colours the strength of M cone reaction will lessen while L increase. Additionally at green colour also S cone will be slightly activated. All that brains receives are signals from those 3 cones.
Now the brain cannot verify what exactly triggered cones. It only knows that those three signals combined tell about a colour of the thing on which we're looking. If it was just a very narrow "beam" (in terms of consisted wavelengths) or the contrary - a broad one, a brain has no way to determine. As a result the same set of "results" from all three cones produce the same "colour" for the brain.
This phenomenon is actually used to artificially produce colourful images, especially on screens (TVs, monitors). Rather than trying to emit all colours, all that the screen has to produce is the three colours to which our cones respond and changing the intensity of those colours it can trigger (almost) any composition of signals from the cones, effectively producing for a human brain (almost) any colour visible to a human.
Unfortunately that's still not that simple as here we step into
To make it short (errmm...), the brain uses its previous experience to get results while interpreting the environment. As someone has described it, a brain is not really experiencing the environment. It's like a general in a bunker. It sits in a dark, humid closed small space and gets information from the outside world through "liaison soldiers" - neurons. Then based on those messages it builds its own interpretation of the world outside.
We will focus on the part responsible for vision. In general, each of wavelengths (a single one) produces a signal on cones specific for itself. We "learn" those reactions when observing a rainbow - either natural (created on droplets of water) or an artificial (created through a prism). Now our brain can compare reaction of mixed colours to those of a single wavelength and distinguish similar colours. It can also notice that there are colours others than those in a rainbow so it has to present us those in a different way. This way we get colours like white, black, purple, brown, grey and others that require mixing various wavelengths.
But that is not all. Our brain also "learns" how different things look like in various lighting. If we have a white sheet of paper and we look at it in various coloured lights it will be changing its colours accordingly into the colour of the light in which it is now. But our brain knows that it is white so despite those changed lighting conditions it will still suggest its white. Now if we do not have other prior experience and to someone who already has seen white paper in a red light we give in a room with red light a red sheet of paper, the brain of such person will assume that it is a known paper and since most sheets of paper are white it will suggest that this specific sheet of paper is also white. Only changing the lighting will make brain change its mind (eventually someone with authority stating that the sheet of paper is now red). The problem is human brain fills in the missing information and it actually captures only a very small part of the surrounding. Similarly when we look at tree needles after the dusk we kind of see them greenish even though what we can see is just grey. Moreover it may turn out in a broad light that they are brown rather than green (this is my personal experience actually)
So in general our brain will adapt the picture according to the lighting. If it cannot determine the lighting for sure it will make a best guess. As a result you have this kind of picture, with question - what is the colour of this dress - white and golden in a deep shade or blue and black in a very strong light?
If you don't know that yet, make your guess and then check e.g. on The New York Times and read more about it on Wikipedia (though probably everyone know by now).
How other species can see
Having said all that...
When saying "white" we can express one of three things:
- something that we can observe in a way that the range of wavelengths coming from a direction of that object (be it emitted, reflected or passed through) triggers a more or less uniform response of all cone types (that's the most common and natural understanding) - physiology
- something that we know from our experience that if put in the typical white light (in reality - Sun light passed through our atmosphere) is known to produce the wavelengths as described above even if at the moment we are observing it in a different light so the actual cones response is different than expected for white objects - psychology
- something that produces wavelengths in (at least and almost) full range of what we call visible light - physics.
If we consider a different species that developed in different lighting conditions we may safely assume that it will have a differently developed sense of vision (if any). If it has a sense of vision it may or may not be colourful. It may also perceive light in a totally different way, e.g. the way we perceive warmth on our skin or smell scents. We may safely assume that if the species cannot perceive colours at all, it will not have names for the colours, however it will still have a name for existence of light or lack of it (it might be gradual). Even more interestingly if the species does not have vision and can only perceive electromagnetic wave through instruments, the naming will be very technical, focusing on ranges of the spectrum, most probably based on some specific properties, in no way related to colours as we know them. So depending on those circumstances we may consider those names that a species might give as matching to some of our definitions of white1 for the species. In other words it may have a name for a light covering such ranges of electromagnetic wavelengths that all light receptors of the species are triggered at their maximum. It may have a name for an object emitting electromagnetic wave in some huge pre-defined range. And it can have a name for objects that are capable of reflecting/passing through the first light from this list if put in the right lighting. Those names may be the same or may be different. And those names may not mean the same range of wavelengths as what we call white.
Let's have a look at some on-earth examples just to give a hint. Then I will give even more extreme options.
Note - I know neither the psychology nor the physiology of other Earth species not to mention extraterrestrial ones (just some fun facts about them) ;-).
Bees are capable of seeing shifted light spectrum compared to us. They don't see the most red part of the spectrum but instead they do see at least some UV (graphics from Bee Culture:
As a result they can see flower patterns that are invisible to us. Note that those pictures have UV filter applied and has the colours adapted to show the additional patterns but of course the "colours" seen by bees are... well, we don't really know how do they see it (BTW we don't even know if brains of different humans present colours in the same way).
While the white as from the Sun will be "white" for both us and bees, if we consider the minimum white range, it will be missing the red part so it will be somewhere between green and blue.
Snake use infrared for vision. As a result they actually "see" temperature of other bodies. On the other hand the colours we see are virtually invisible to them.
Again a white light will be white for both us and snakes. But both our "minimal white" will be black to snakes and their "minimal white" will be black to us. To be more specific, our vision spectrums slightly overlap but for the sake of example I'll ignore that part as rather irrelevant part.
This is how supposedly snakes see:
Moles have very poor, monochromatic vision. I couldn't find the spectrum, but in general they see light. A speaking mole will probably have a single word that will be a combination of what we call "white" and "bright". It will not understand what you're talking about when you refer to colours unless you use physical properties. For such mole any colour we see can (if intense enough) be perceived as "white/bright".
Well, this case is closest to your expectation. Mantis shrimp live underwater, where the light is limited to mostly blue-green as the rest is quite well absorbed by water. Still those shrimps have 12 photoreceptors which allow their brain to do far less visual processing. They probably also see a broader range of colours.
While for humans "white" requires as little as 3 wavelengths, for shrimps it will require an outstanding 12 different wavelengths. So something that we can already call white will be some colour for a shrimp. On the other hand shrimp's white is white for us as well.
Extreme extraterrestrial forms
I would say sky is the limit. Let me just give you two extreme examples.
First will be a species which developed various photosensors that are combined with other types of senses. These work a bit more like a shrimp - i.e. they are specialised not to see as we understand it but rather to quickly recognise various opportunities and dangers. Combination of specific colours and scents produces a signal "food" to a brain of this species while combination of specific colours and heat produces a signal "danger" (fire). For such organism there will be no such terms as colours. If it does not perceive light as a separate stimuli (due to evolution from mantis-like perception into even more specialised, with recognition of signal meaning moved to receptors and brain able to quickly react to it, but no separate vision and only later development of cognition) it will not be able to communicate in terms of colours or light as we know it. Assuming it will grasp eventually a concept of electromagnetic wave it will have some sort of scientific, technical word describing what we may resemble as white (with either broader or narrower range), however I don't know if there exist a single word for a beam covering all X-Ray wavelengths in any human language so it might not be a word, but rather a description of the observed/potentially possible physical phenomenon.
On the other hand they will have a very complex structure of terms for various things related to perception completely impossible to understand for us. It will be like saying "I perceive a light morning breeze full of tasty aromas incoming" in just two or three words.
Second example will have a human vision similar to us in terms of way the perception is done but due to various conditions developed in radio frequencies. Those aliens will be reading our radio communication by seeing it as colourful patterns changing quickly. But what we consider white light will be completely impossible to "see" for them. On the other hand if they present us their "white light" it will be invisible to us but we will hear a more or less uniform noise in our radio receivers. Yet they will probably have wording developed in somewhat similar manner to ours, just meaning completely different wavelengths of electromagnetic spectrum.
1 It's worth adding that the name black can have meaning so far from our natural understanding of it as "lack of white/(almost) no (visible) light coming from the direction" that the Sun in astronomy is considered almost a black body. See this question for more details.
Sorry, it came as a very long answer but I hope it gives a bit better understanding of the problem.