This woman was continuing to confuse him. She was almost determined to, it seemed. She said that she wasn't planning on buying them drinks because she wasn't the age to do so. So why did she say, "Drinks are on me?" It was utterly confusing the way Americans spoke.
He sat next to her as she ordered, and when the bartender looked to him for an order, he raised a hand up, the universal indication that he didn't want anything. It was then that she asked him what she should call him, or what his name was, probably. He looked at her, his lips forming a line. "Suzaku," he finally said, before returning to facing forward.