That's actually what they're doing. The reporting said timezone when the actual order is more about time standards.

They're creating coordinated lunar time, as a complement to coordinated universal time, so it's a different time system with details about how it relates to UTC.

https://www.whitehouse.gov/wp-content/uploads/2024/04/Celestial-Time-Standardization-Policy.pdf

Timezones on the moon don't serve as much function, because the day/night cycle is closer to a month long, and doesn't map to human rhythms at all. In a hypothetical where we have moon colonies on opposite sides of the moon, there's no reason for them to not still have synchronized day/night, since it already has no relation to the movement of the sun in the lunar sky.