I guess the OP was imagining James Bond flying in to some third world country and meeting with some shady types and when asked his name goes “Bo…I mean, Smith! Robert Smith! Yeah, that’s the ticket! I am not a spy, seriously why would you think that!”
Like, he knows he’s not supposed to give out his name of James Bond, world famous international super-spy, so he has to improvise a cover identity on the spot and hope the thugs never look at his wallet which contains his spy agency ID card and laminated license to kill. Kind of like how before you sell someone cocaine, first ask them if they’re a cop, which will totally work.
I have no useful or authoritative answer except to agree with those who say they simply present their documents, real (under legitimate cover) or fake (if you are an “illegal” agent with a made-up cover). “Trust what you built,” as one character in a movie said to police undercover agents trying to infiltrate a Columbian drug cartel. Reluctance or delay would only bring on suspicion, which you don’t want. I would guess a lot of training and psychology go into how to behave in such situations.
On a less useful note, in the movie “Atomic Blonde,” set in Berlin just before the Wall fell, a British agent caught in a compromising situation in East Germany by two East German police fumbled to pull out his wallet, and fast talking in a overly-friendly manner approached them digging for i.d. in his wallet – then dropped it clumsily right at their feet, exclaimed “Oh!” and as bent down to retrieve it punched one of the VOPOS in the testicles with an uppercut, putting him out of the action. Without hesitation, he went after the other, catching both completely by surprise, punching him in the face and putting them out of action in short order. Well, that’s one way to do it.
I don’t think American police will appreciate that response, however, so you’d better know what you’re doing and be very serious in your commitment to it. Probably it’s better to stick to ACLU guidelines in such situations if you want to resist.