VSauce has an interesting video where he talks about the two established, international organizations who are already set up to handle this, SETI and the UN Office for Outer Space Affairs.
While the UNOOSA denies having the authority to speak for Earth, if aliens show up the expectation is they'd be the ones everyone would look to coordinate our response. In a panic, governments like using established structures who have been thinking about the problem for a long time. The UNOOSA would look to SETI for help, who have been thinking about and waiting for this for a very long time. SETI has developed a plan "following the detection of extraterrestrial intelligence" which would likely form the framework for our official response. It includes...
- No response to a signal or other evidence of extraterrestrial intelligence should be sent until appropriate international consultations have taken place. The procedures for such consultations will be the subject of a separate agreement, declaration or arrangement.
Their official line is to keep quiet until we all talk about it. Assuming they agree, that would keep all of the major governments and institutions quiet (if they don't agree, then there is no legitimate official communications). That covers nearly everyone with access to a powerful, directional radio antenna. Maybe Earth will have to come up with the Intergalactic version of "please hold, your call is very important to us..."
What about rogue signals? Anything below a certain amount of power will be lost in the noise. What noise? Our noise. We emit a lot of electromagnetic noise into space. Some of it is chaotic, but a lot of it is patterned... communications. However, it is all patterned differently as we use dozens and dozens of different protocols. Ironically, some of our most important communications will look like random noise because they are encrypted. The aliens will have been observing this for some time as they approach. If they do not understand the content, they will understand that it is intelligent. However, the overall pattern will be chaotic from many sources and in many forms.
Whether or not they will recognize this means we are not unified is speculation, but they will recognize that random electromagnetic chatter is normal. Having some yahoo bounce the digits of Pi off their ship with a relatively low power laser isn't likely to seem out of the ordinary.
Nor are they likely to communicate anything intelligible to the aliens beyond basic math, not before the rest of the Earth gets its act together. We don't know what part of the electromagnetic spectrum they're observing, how they're using it (AM or FM or something else?), or if they're even using electromagnetism at all! If they knew how to finely manipulate gravity waves how we manipulate EM we could be staring dumbly at each other for a while.
The only rogue nation with a space program capable of powerful communications is North Korea (Iran could probably do it, but they're not as rogue as the US paints them to be) who would be the wild card. However we're safe in that North Korean scientists are not going to crack the code before everyone else does. We're double safe in that the messages will likely be internally politically focused narcissistic gibberish. "Here is a JPEG of our Dear Leader!"
When Earth responds, they must do something out of the ordinary to get noticed. They must order the chaos, that's a clear sign of intelligence. Individual governments and institutions, guided by the UN on the advice of SETI, would all point their transmitters at the alien ship and simultaneously broadcast the same message. This is unprecedented in the history of humanity. One group transmitting with the most power is like shouting "LISTEN TO ME, I AM THE LOUDEST", but having multiple sources all over the planet sending the same signal says
Listen to us, our voice is unified.
