There is no problem renaming the style as it has not been released yet.

Maybe we should claim the style for internal use only and name it_mpl-gallery?

I can see arguments both ways. We use it as part of the user-facing docs so we should be able to change it at will so it should be private, but people may want to mimic and track the style and hence it should be public. Maybe a note someplace that we consider this style volatile?

I can see arguments both ways. We use it as part of the user-facing docs so we should be able to change it at will so it should be private, but people may want to mimic and track the style and hence it should be public.

Both are not possible at the same time, in particular if change includes rename or delete. I don't see why it is critical for anybody to exactly track the style. It's not the end of the world if somebody copies it and doesn't immediately realize when we change. If they still want to track, I think setting up a CI up-to-date check on their side is the correct choice.
For now, I'll be defensive and claim the style to be explicitly private. We can always publicize it later when a compelling reason arises.

Anyone should merge once the build is done.