Not sure when this was added, but if you rename your group to a different name then the previous group name can be taken by someone else and not appear on the group page.
From personal experience I spent lots of robux creating groups and changing their names as making a whole other group took longer to swap and change (100 group max) and to save time I just changed the name and I did this to gatekeep the name to use for the future so now all those names I changed are just gone and just sort of a big waste, im dissapointed.