"Well, I hope I'm making the best impression right now." So saying, he claps his hands together. "After all, it wouldn't do well for me to mess up a great encounter like this!"

This girl with her way of speaking really seemed like the formal type. In that case, he should be just as formal, right? He gestures to himself, a flourishing move as if he's putting on some sort of show instead of just giving a casual introduction.

"In any case, would it be rude to ask for your name?"