"James Bond" is a code name that comes with the 007 ranking. This originally started as a joke to "explain" the different actors that have played him. Now it causes debates that can rage for hours, and explanations on how precisely it melds with the films' Canon extends into Wild Mass Guessing territory.
The corollary to this theory is that Felix Leiter is likewise a code name within the CIA.
If you must include Daniel Craig's Bond, there's even a relatively easy solution. Time travel!
Ian Fleming intended for Bond to have died at the ambiguous end of From Russia with Love. His recovery was all off-page, merely stated by M at the beginning of Dr. No and never touched upon in Bond's internal narration. Here's where the code-name theory hits the books.
Some of the classic characters even appeared as unlockable characters in multiplayer modes of video games based on the Pierce BrosnanBond movies. Assuming the Brosnan Bond movies are in a separate continuity of their own.