BuddyPress.org

You can, but it requires a few, little ninja hacks!

“my-groups” is hardcoded in /bp-groups.php in v1.2, however you can remove the current navigation for my-groups, then add it back with your custom slug.

Read this thread for pointers:
https://buddypress.org/community/groups/how-to-and-troubleshooting/forum/topic/hide-general-settings/

It uses the settings page as an example, but you should be able to get the gist of it.