Re: Changing the group name
Admins can change the name of their groups because they are the rulers of their little kingdoms. If you don’t trust the admin – don’t join the group.
Of course there are many ways to look at the group functionality. For my part, I see the group as a community within the community – a place where a few people can coordinate something, discuss something, or whatever. A group has it’s dynamics, and part of that is being able to change. Perhaps the “Event X Planning Group” will later take on a new event and thus change their name to “Event Y Planning Group”, or perhaps they’ll just bask in their old glory and rename the group “We who were behind event X”.
Another way to see the group functionality is the way they have evolved on Facebook – a sort of name list, each group a statement on a particular issue, with no function other than to be spammed and show up on profile pages.
If you prefer the latter, I can understand your predicament. A plugin can probably be built to provide the functionality you are looking for.