How would astronauts and citizens of Mars and beyond tell the time?

With a clock set to Coordinated Universal Time (UTC)

UTC would be the logical measurement.

It takes about 24 hours for Mars to rotate, so there would probably be time zones as on Earth. Of course someone would have to keep track of Earth time for the purposes of interplanetary communication.

We’d set up new time zones for Mars & earth’s Atomic Clock will keep up with it. How else will the government be able to track us???

Stardates.

They will wear digital sundials strapped to their wrists coordinated with the Greenwich time signal adjusted for a 3:03 time delay. There will probably be an app for converting Mars years into Earth years and vice versa.