[itsme]

All groups (Genres, Composers, Setlists, Albums, Types, Custom Group...) work the same: long press, set the checkbox of the group item that you want to change, then select "delete", "rename", "copy"
The songs that the group contains react as expected: If you rename a group, the songs are still members of the group, but show the new name. If you delete a group, it is removed from the songs that it contained before. If you copy a group, you are asked for the name of the newly created copy, the copy contains the same songs as the original. The songs are not affected otherwise.
E.g. I renamed all the Source Types according to my personal preferences