I've asked myself the same question, if anyone ever brings up my old name or my situation. My philosophy is the less there is to say, the better - so maybe "oh, they must have confused me with someone else." I remember one time I went up to a girl who I swore was my friend Julie, and said "Hi Julie!" and she went "I'm not Julie." I still to this day don't know if it was Julie playing a prank or not, lol, but yeah.
You could also just say "that used to be my name" and hooope they don't put the pieces together and leave the "mystery" be. It's a hard call. Ultimately, you have to do what feels right in the moment.