Just wait until every country’s base uses its own capital’s time. The time zones won’t even be in vague order around the moon like they generally are on earth but distributed randomly based on whatever country has the biggest base in the area.

Worse, if different countries bases and teams are using different home time zones than you don’t even have time zones. Two people from different countries in the same room could be different time zones, purely based on the country they work for.

If this fails and everyone with a space program can’t agree to just use the same standard, then time zones could get very, very bad in the future.