How do they keep track of time in Star Wars?

They don't need to; It's pure fantasy. Star Wars makes no attempt to be consistent with laws of physics because it's simply not relevant to the film's objective. Its aim is to tell a story and therefore has no obligation to be accurate in any frame of reference.

In theory, time is exactly the same time everywhere.
It is distance that makes the difference to an observer.
So with the vast distances used in the Star Wars fantasies, time dilation would come into effect.
Especially with light speeds.
No matter what speed you are going, the time passed on the journey would equal the time change at your destination.
It is not exactly time travel, just physics.

In a similar way to how international organisations coordinate on Earth and in space.

Each planet observes their own time and calendar system for local use, but uses a single system for use in space and inter-planetary contact. In the case of the Star Wars galaxy, the calendar and time system of Coruscant (the traditional galactic capital).

Convenientally enough, one Galactic Standard Year is almost exactly the same length as on Earth, with 24 hour days ;-)

Most science fiction universe assume the existence of a standardized unit of time, usually enforced by treaty or empire.

Star TREK never explained it but they dealt with it: "Captain's log, Stardate 2077.5.................." That they realized this and made up some universal timing, date system. Of course, we won't actually do that until if we have need to.

Sure. But, just like we know a day on Earth is 2 1/2 days on Jupiter, they convert to the proper units.

Great question!

by deciding a common and a specific dating

How do they keep track of time in Star Wars?
They don't , it's a fantasy, time dilation would not allow any of the characters traveling separately to arrive anywhere near the same time at any given point in space.

Parsecs apparently, here it is a distance.

SMPTE code.

Star Wars is a MOVIE, and that is how they keep time in the moviews

They don't, it is in fact "Because the script said so"