Indeed. Different names might be used for notes depending on what key you want to write in.

For example--[he plunks down the B-natural key] This is B-natural. However, there's no black key next to it. Only the C-natural. However, depending on what key you're writing in, it could also be B-sharp. [lol here's the beginning of music theory looks ordered on the outside but can be chaotic and ridiculous]