As the saying goes, 'if it ain't broke, don't fix it'.
For any long and well established group, with more than a couple of members and 'real' messages, I would suggest a name change is more trouble than it's worth (unless it's really worth an awful lot!) - it will have a Pandora's box (its own!) of issues waiting to jump out and bite you.
And from memory of when I tried it, deleting the last subgroup, changing from a group with subgroups to one without, did reveal issues when I tried it - searching this group may reveal more, if I raised them at the time.
Jeremy