Hi, I'll get to the point. This character has been sent on a mission where he is to use a name which isn't his own, so obviously the people in this place won't know his real name. When he is to engage in any conversation with these who don't know his name do I write 'said -real name-' or 'said -fake name-'. I just don't want readers to become confused and think there are two characters. Thank you in advance.
I currently have a character that calls another character by a name that is not her true one, but I always tag her with her true one. I think it makes it clearer in the reader's mind that who he thinks she is, is not who she is.
You could also give your reader a reminder every so often if you think it's needed. "I don't know," Chris said after a pause, mentally reminding himself that tonight, his name was Martin. Chris heard the guy calling out 'Martin' and it took him a few seconds to register that was him. "Thank you, for your more than generous offer," Chris said in Martin's thick southern accent.