The fanboy in me still gets goosebumps when the film finishes with that line.
Another part of me feels it's bit self conscious. Does it really fit where it is? I guess I never got a great feel for the whole transition business. Bond doesn't seem any different to me on the boat, talking to M at the end, than he was talking to her in her office at the beginning. Why is he Bond, James Bond now suddenly?
Because he's become Bond, James Bond. It's kind of the whole point of the film, innit?
Go back to the beginning of the movie, he is supposed to bring Molloka in for questioning, but ends up killing him. It's a major screw-up, he's just following his instincts rather than thinking ahead, and he soon does this again when, out of anger he plans to walk up to Le Chiffre and stab him, which would be a repeat of the Molloka incident and would probably signal the end of his career, and maybe his life too. MI6 want Le Chiffre brought in alive for the information he has. But another agent, the wise, cool, and probably a little more experienced Felix Leiter intervenes and stops him.
Bond has good "spy instincts", like tracking the cellphone signal to the Bahamas and getting to Dimitrios, and this is probably what M saw in him when she promoted him to 00 status, but he hasn't learned to think ahead. Ironically, its Le Chiffre who clues Bond in as to "the big picture". Killing one man won't solve anything when you're dealing with a sprawling network of terrorists, the big prize is getting the information he has. His experience with Vesper only solidifies this - he ends up with a bunch of dead goons in Venice, but no answers. This time its personally affected him - all the people he just killed are now useless, he could have gotten some information out of them about Vesper, the money, and the organization etc, but they're all dead.
When he finds Mr. White, the Bond at the beginning of Casino Royale would have aimed the sights higher and blown his head off. The wiser, experienced 007 knows that this bastard is more valuable alive. It took a personal tragedy for him to figure it out, but he's finally Bond, James Bond.