I'm making a new world in the near future and its my first time. I've downloaded Custom worlds and the names of the Rabbit Holes change. Like the Sunset Valley hospital is Sacred Spleen and a CC version is the same hospital but with the name Fransico State Hospital or whatever. How exactly do I do that?

I'm pretty sure NRaas DebugEnabler has the option, someone will hopefully correct me if I'm wrong.

Does investing and renaming it work when you're building another world, or would you have to add it in-game from the lots bin?

I kind of think none of these suggestions apply to CAW. I don't know how it is done in CAW. You might get the attention of a CAW expert if you go to the Create/CAW subforum. That's what I'd try. But be patient.

I don't think it's possible to rename the actual rabbithole building in CAW, unless you use a custom rabbithole. The override name seems to be stored in the savegame, so you can have a sim buy the lot and rename the building in-game, but you cannot do this in CAW.