There are purists out there who think there's one Bind, but I'm with you. I think the last movie even mentions assigning "double-oh" numbers that were...suddenly available.
I don't know if that was Fleming's intent or not with his series, but the movies are such a force of nature they are more canon than the books.
If they announced Idris Elba as the new Bond I wouldn't flinch. I would, not that it matters, refuse to see "Bond, Jane Bond" if that's where they take his identity. In our "all or nothing" belief system these days I guess that make me a hypocrite?