No, the moon’s rotation isn’t on a 24-hour cycle. I’m not an astronomer, but I pretty sure since it’s tidally locked to earth and on a 28-day cycle around the earth, a lunar day is actually 28 Earth days, but I’m not actually sure how that would factor into the number of time zones (I’m pretty sure it would be more complicated than just 24 time zones to match 24 time zones on earth, though).
Plus, I think the speed of the moon relative to the sun is different enough from Earth that you need to take relativity into effect, which is the real headache here.