You can set a universal time standard, that's planet-independent, and can be applied to faraway galaxies that aren't able to keep track of the rotations of a distant planet, by using universal physics time-based constants to keep track of time.
The way we do it, currently, is by creating microwave pulses whose frequency is a rational fraction of the caesium-133 isotope. Caesium-133 has a hyperfine energy excitation in its ground state whose energy difference is equal to that of a photon of light whose frequency is exactly 9 192 631 770 oscillations per second. (It used to be extremely close to that integer number, but since then we have redefined the second so that it is an exact integer.) So, when tuning a microwave signal to the exact frequency needed to excite Cs-133 in this particular transition, the signal can be tuned to 1/9192631770th its original frequency, and we take its pulses to be "seconds".
In principle, instructions for this procedure can be given to a distant galaxy that cannot keep track of Earth's rotations, and they would have the exact same unit of "seconds" that we do. And if we don't want to define longer stretches of time in an anthropomorphic sense, we can use nice round numbers instead. For example, a "day" can be 100 000 seconds instead of 86 400, and a "year" can be 50 million seconds, instead of 31.536 million seconds.
Another way to do use universal physics that's not locally dependent is to describe everything in terms of large multiples of Planck times. One Planck time one unitless value of time in "natural units", where universal constants $c$, $G$, and $\hbar$ are set to 1. (The above units are the speed of light, universal gravitational constant, and reduced Planck constant, respectively.) Physicists work in natural units all the time, as a convenient way of saving them a lot of time writing symbols. When that happens, time, distance, etc. are basically unitless numbers.
Again, conventions can be made for talking about large portions of time. For example, we can define the "day" to be $10^{48}$ Planck times. (Clearly each species would make a name for it; they wouldn't say "I'm leaving for my trip, I'll be back in $6 \times 10^{48}$ Planck times.")
The advantage to Planck Time, over Cs-133, is that the latter is a far more arbitrary choice of measuring time than the former. The constants $c$, $G$, and $\hbar$ are universal, and far more broadly descriptive of general physics than an extremely specific multiple of an extremely specific atomic energy transition. If we ever made first contact with an advanced alien species, and started talking about durations with them, we would most likely talk about elapsed durations in terms of Planck times.
I would keep in mind that it's convenient to talk about time in terms of your planet's rotational cycles. Especially if you're biologically tuned to sync your sleep cycles with the rotations. That's how we mentally keep track of time in order of days. If you had an event set for 8 days from now, but one "day" was, say, 0.7 rotational cycles of your planet, it would be mentally confusing to track when the event is, and you'd have to do the math. So while the above standards can be adopted as a universal standard for communication with people from other planets, people from the same planet would still probably talk about time in terms of their own rotational cycles.
