The James Bond codename theory doesn't work for a couple more reasons. The Bonds played by George Lazenby, Roger Moore, and Timothy Dalton were all either shown or stated to have been married only one time, and the wife was killed (the fate of the wife of Dalton's Bond is less clear, but obviously something bad happened). I suppose supporters of the theory could say that it's the product of a doctored standard-issue dossier for later Bonds, but that doesn't make sense because both Moore and Dalton are visibly upset when the spectre (no pun intended) of Tracy is raised. Also, the Felix Leiter of License to Kill explains that Dalton's Bond was married a long time ago. So really, the only option is, "it's a big coincidence.'
Also, George Lazenby is supposed to be Connery's Bond -- the whole pre-credit sequence/early scenes at Universal Exports go to great pains to say, "Hey, it's still the same guy, we swear!" even going so far to use the theme music from previous films when Bond is cleaning out old trophies in his desk drawer. Yes, they inserted the line, "This never happened to the other fella," but that's just a joke they put in for shits and giggles.
Timothy Dalton's Bond is good friends with Roger Moore-era Felix Leiter played by David Hedison. (If James Bond is a code name, I guess "Felix Leiter" would have to be, too -- although according to this logic, why would David Hedison be allowed to resume the "Felix Leiter" identity when it's already changed hands? He wasn't the first (Jack Lord), so you can't say he's "the real Felix.")
Bond in Die Another Day remembers all the old gadgets that Connery's Bond used.
But most importantly -- let's say Bond is a code-name used by agents who achieve "007" status, and they all happen to be womanizers with a propensity for bad puns who introduce themselves surname first, [dramatic pause] followed by their full name. Okay, let's pretend that's logical -- why would every single new 007 agent like Vodka Martinis, shaken not stirred? And order them that way? I don't think that's something MI6 would care to replicate in each agent.
I just think of Bond like superheroes in comic books -- all the adventures "happened," but it's up to you to decide how you want to reconcile (or not reconcile) the continuity quirks.