Granted, my second suggestion, that the new incumbent takes the name for plot reasons but decides or is compelled to keep it, may be more plausible.
My post was really just to give some examples of how it could be done as a plot device, there may be other ways also (but probably not he dived off the submarine base roof just in the nick of time...)
One way or another they will find a way to bring the character back - indeed they will have already decided how it can be done. James Bond is far too lucrative to ever really die.
I didn't stay to the end of the credits, but perhaps they still said "James Bond will return", because he will.