The problem you are dealing with is one of assumed continuity. Is this version of the story directly linked with previous versions, or is it a retake, a reboot, a new unconnected version, a different universe? That is a common problem with series that are carried out over a longer timespan than the characters should be seeing.
Example: the Tom Clancy “Jack Ryan” series. We get the first story, The Hunt For Red October, with Jack played by Alec Baldwin, set in 1984. Next, they shoot Patriot Games, and cast an older Harrison Ford as Jack. The story is set about a decade later, so the aging works and the story sequence works, so it can be assumed to be a continuous story, a continuous character portrayed by a different actor (the “Soap Opera” effect). Follow on with “Clear and Present Danger” with the same actor.
Then they want to film Sum of All Fears, which has a setting later than those other stories (2002), but for a variety of reasons want a younger main character. Ergo, you are left with a discontinuity - How does Jack Ryan who stole a submarine in 1984 get to be a young man again in 2002? Answer? You reboot - the character is Jack Ryan, but in this universe, Jack is just starting his career, so the other stories did not occur for him. You have to agree that continuity is not preserved, that this is a completely new “Jack Ryan” series.
Similar situation is the described Batmans. The Adam West Batman has no continuity to the Micheal Keaton Batman, who has no continuity to the Christian Bale Batman. However, the Michael Keaton Batman is supposed to be the same Batman as Val Kilmer and George Clooney. Those four movies have continuity.
So with James Bond, we see the same issue surface, primarily because of Bond being initiated in the 60’s Cold War and lasting to the new millennium. Somewhere along the line, that continuity is broken, and the “James Bond” we get is a new James Bond in a new universe, not necessarily the same Bond.
However, what makes it more complicated is keeping many of the same actors in their same roles to cover that timeframe. There’s no reason to doubt that Connery, Lazenby, and Moore are the same James Bond in the same continuity. There is some reason to question Dalton as being the same Bond in the same continuity, and that gets more troubling to accept Brosnan as the same continuity.
However, there is a clear reboot with Daniel Craig. This is a new agent at the beginning of his career, set in ~2006, having no relation to the James Bond of the Cold War. It is also stylistically different than preceding Bond movies. The only source of complication is retaining the same actress who was “M” in a couple prior movies. That suggests there is continuity that is not otherwise present.
A similar situation arises with characters like Bart Simpson, who has been a perpetual 10 year old boy for over 20 years. At this rate, he’s almost had more screen time than actual time he could have been 10. Suck it up and ignore it, continuity isn’t the point of the story.
None of which precludes the possibility that “James Bond” was a fictional cover name given to the agent that Daniel Craig plays upon becoming a spy, as opposed to whatever real name he had as an orphan or going into the military. But nothing in the overt text indicates Bond as an alias provided to him, as opposed to “James Beach” that he was briefly styled during Casino Royale to enter the poker game. Then again, Casino Royale explicitly stated that “M” was not a random code letter assigned to the head of Operations Branch, but actually stood for - oh wait, she didn’t let him say it. But that almost certainly is a new creation for this incarnation of Bond.
A similar situation arises with regards to the current TV show, “Nikita”. As I described it in another thread, it draws elements from prior incarnations of Nikita, but is a new dip into the well of Nikitaness. It’s a completely new incarnation, just has a lot of points of overlap. It is not meant to be continuous with any prior incarnation, such as the Peta Wilson version.