"James Bond" is a code name that comes with the 007 ranking. This originally started as a joke from the returning Sean Connery as Bond in Never Say Die, to "explain" the different actor, George Lazenby, that had played Bond for one film (the company who created Never Say Die only held copyright for an early Thunderball script, not the Bond franchise in general, so it skirts the edge of canonicity). 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 and the reasons why MI6 set it up.
The corollary to this theory is that Felix Leiter is likewise a code name within the CIA.
The other popular explanation for Bond's different appearances? Time Lord. Each incarnation is a new regeneration, emphasising some personality traits and downplaying others (How exactly Diamonds Are Forever fits in is left as an exercise to the reader. Perhaps he was "revisiting some old faces"? ). You can even argue that he has a Time Lord-esque title -the Doctor, the Master and... the Bachelor. note As in academic degrees, if you're not familiar with the terminology.
If you must include Daniel Craig's Bond, there's even a relatively easy solution. Time travel!
Each different incarnation of Bond lives in an Alternate Universe, with some events such as the death of Tracy happening in most of these universes out of In Spite of a Nail (while Daniel Craig's Bond never had a Tracy at all, he still ended up with a Lost Lenore). Also, Bond exists in a different decade in each universe, Bond might have been active solely in The '60s in one and solely in The '90s in another, but there will always be a Bond per In Spite of a Nail.
Although Dr. No's SPECTRE number is never explicitly stated, common fan consensus is that he was Number Four, since Kronsteen, Rosa Klebb,Emilio Largo, and Blofeld are stated to have been Numbers Five, Three, Two and One respectively, and it would make sense for Bond to face SPECTRE's top agents in ascending order of importance finishing with Blofeld himself.
Book-based Fanon
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.
Most of the films are often referred to by their acronyms, i.e. TLD for The Living Daylights. More amusingly, this is why The World Is Not Enough is sometimes referred to as Twine.
Examples should be tropes that show up often in fanfic which are not just taken purely from canon:
Patchwork Fic — Classic!Bond villains and events being referenced/included in Reboot!Bond's backstory. (Alec Trevelyan is particularly popular for this).
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.
