This is certainly the trademark phrase, even if not legally “trademarked.” (Is it?)
Like so many branding elements of Agent 007, this one originated with Ian Fleming. As a matter of fact, it appears in his first James Bond story, Casino Royale
Bond had a feeling this might be the CIA man. He knew he was right as they strolled off together towards the bar, after Bond had thrown a plaque of ten mille to the croupier and had given a mille to the huissier who drew back his chair.
‘My name’s Felix Leiter,’ said the American. ‘Glad to meet you.’
‘Mine’s Bond — James Bond.’
Casino Royale, chapter 7: “Rouge et Noir.”