I think it's not convenient for users to rename or remove profile now.
Why would you rename profiles?
Once may be, after a mistake, but more then once to justify the UI change / feature request ?
Well renaming is not necessary, but how about removing a profile? As far as I know there is no UI for it.
On the device .... Go to the location of your profile folder(s), remove the unwanted profile.
A button or menu for removing it is more convenient.