If we're to make it conjectural, it makes sense to align it with the other conjecturally named Dark World.
I feel like that one could work well as "the closet world" too.
It flows much better in text, while also making sense and clearly being conjectural.
I think that adds unnecessary ambiguity. "Closet Dark World" makes it very clear that it's a Dark World inside the closet, but "closet world" removes an established name (Dark Worlds) in place of minor conciseness, which in my opinion is not any better. Same with classroom world vs classroom Dark World.
Agreed with Shadow here. All these other options are too vague.