Renaming pages works fine. However with renaming a group no access right entries that have been set using the former name of the group are updated. So one ends up to have to go through all access right entries to remove all references to the old groupname and add the new groupname.
The rename functionality should check whether it's renaming a group and replace any reference to it in the access right entries.
I can image the same problem arises when renaming users, but haven't yet been able to check whether that assumption holds.