Currently, Moon missions adopt the time zone of the country responsible for the mission, for ease of communication back to Earth.* As each country has a time zone referenced to UTC, so time is measured on the Moon relative to UTC as well.

As the Moon gets busier, communication between points on the Moon presumably becomes more common. It may be more convenient to have an independent standard based solely on the Moon, which would not reference Earth time. ESA, in particular, has expressed interest in this:

https://www.esa.int/Applications/Navigation/Telling_time_on_the_Moon

Would a new standard apply a single standard time to the entire Moon? Or would the Moon be divided into time zones like the Earth?

Market Resolution:

Market resolves according to an agreement between a preponderance of relevant national international agencies by 2030.

0: No independent time zone agreed. Current status quo of referencing UTC continues.

1: One independent standard time for the whole Moon.

2+: Moon is subdivided into 2 or more independent time zones.

*Or so it is reported. I'm not an expert, and I can't find details easily.