The Craig series is a new continuity that merely pays homage to the old one. The 1964 Astin Martin is won by Bond in Casino Royale, tricked out with guns and gadgets sometime after, and makes another appearance in Skyfall.
The only truly confusing link to the previous series-- which is a different continuity-- is the use of Dame Judy Dench as M. Otherwise, no actors cross from one series to another. Either way, the M of the Craig run is not the same M as in the previous Bond series, despite being the same actress from the later films in the previous series.
Felix and Moneypenny are also both obviously not the same people as the ones in the previous series. This continuity's Bond doesn't even meet Moneypenny until Skyfall.
So, James Bond is the man's ACTUAL NAME. It's not a code name. He is not a timelord, but a man who became 007 in the reboot Casino Royale, continued that adventure in Quantum of Solace, and then reached a later point in his career in Skyfall.
The previous, other continuity's Bond (Connery, Moore, et al) was also not a timelord, but an agent who was with MI6 from the 1960s until 2002 in Die Another Day. There was always a science fiction element to Bond films (look at all the gadgets and the schemes of the villains!) so it's not an amazing stretch of the imagination to believe that he was the recipient of some sort of "super soldier" serum that slowed his aging and made him a bit more durable than a man who took those kinds of bumps should have been for so many decades. Either that, or you can assume that Brosnan's Bond was really supposed to be an elderly man in his late 70s or 80s, but was poorly cast. And why did he look different from time to time? If you really need an in-continuity explanation, think "plastic surgery"-- He's a spy. He needs to change his look after a while, and MI6 has top specialists who can re-sculpt a man's face (and figure!)
But make no mistake: Daniel Craig's James Bond is NOT in the same continuity as the previous James Bond films.