A cautionary tale: one year we were experiencing some friction around younger children perceiving their classroom name wasn't as desirable as the older PreK's (no doubt the older PreK's fanned the flames on this issue.)
In a highly democratic fashion, we teachers thought it would be both fair and educational to build a ritual around group naming into the beginning of year traditions; each group would go through a process to discuss and determine their group name for the year.
The students loved this idea, and enjoyed the process thoroughly, though we had to vet some pretty weird ideas.
The hitch in the plan? Adult brains. We couldn't shift from year to year, our brains were stuck on the old names and we kept getting it wrong. Of course it was a great joy for the kids to constantly correct us, but we were mired in an unproductive process.
Advice: think of names that are easy (not too many syllables) but hard to ascribe hierarchical value to.