Is this child really arguing with him over his name? If that weren't irritating enough he seems to be under the impression that he's a fictional character. To which, Sherlock has no real idea of how to respond.

"I can say with certainty that I've never been aware of sharing a name with any sort of fictional character. But regardless of that, I assure you that is my real name. Whether or not you believe it is on you."

"But think about it, really think. Can you come up with any reason I might have to lie about my name?" If he says yes then that just means this kid is paranoid.