How are you renaming your initiative? If you do that in Hub (Settings panel) it should rename the groups and items associated with the site / initiative. The name restriction is on the groups which is what we check for uniqueness....so if you can remove the conflicting group you should be able to reclaim the name. I think the search for conflict names is fuzzier then we need it to be which we can look into.
...a similar story is true for deleting. If you remove things you need to make sure you get both the groups & the items and if you do that manually then the domain is left behind. Deleting is best done from the "..." in the site editor.