When I go to my custom themes by clicking "Change Theme" in the inspector, I can't edit the names or delete or anything.
That is the correct operation of Keynote, presumably to prevent users deleting themes by mistake.
The preferred method of deleting unwanted themes is: File > Save Theme > Add to theme chooser > right click and select Delete
This also solved my problem of not being able to save a new master slide as part of a custom theme.
Creating new Master Slides and Themes confuses most people;
to produce a new master slide:
go to View > Edit Master Slides
right click on one of the master slides in the Navigator panel and select New Master Slide or duplicate one of the existing Master Slides
make changes to the new Master slide and rename it by double clicking the slide label
to have the new master slide available to all new presentations it has to be saved as a new theme; (File > Save Theme)