So as it turns out, we can't actually change the group name.
Supposedly we are meant to be able to change the tag, but I haven't figured that one out yet.
Unless anyone is ok with this cringey ♥♥♥♥, we can actually change the name if we contact steam customer support, but it's a one time deal. So, either:
-A: We vote on a name and tag to stick with forever

-B: We just make a new group.
or
-C: Forget the whole group thing.

Your call guys and girls,
-SGT Ping.