Holmes says
M of group seth 2016-02-12 18:49:18 [item 19948#45391]
WTF thumbs down

Seth says
Thorin of group da 2016-02-12 19:06:08 [item 19948#45395]
Incidentally. I am not personally for willy nilly group name changes, even though it is now supportable.

Group names are the golden eggs in this landscape. I would grant them as prizes and sell them and give a few away compassionately to hard luck cases. I would tend my group names in a thinking.domain like a Gardner tends his crops, growing a community out of what people are willing to do and build and bring in to get a golden egg of their own. Group names would be the gold standard currency of my thought.domain empire.

And for recreation, fun, and personal expression I would let people play to their hearts desire in pennames, becoming a different inspired creation in every moment, as they want, while the system keeps order and identity intact and well known under the flying artisans thinking themselves anew with their comrades across the domain.
yes that’s kewl cool … and grabbing a “identity groupd” prename would be fun and lucrative to gameify as you have noted.  Perhaps that game itself can be configurable.  One option might be to move the “identity group” to the first “sign up” form and check for collision at submission time.  Or even if there is a collision assign the numeric permalink and let them make up a identity name later.