Setsuna was raised by wolves-- well, actually by terrorists, so things like manners and proper social etiquette were foreign concepts to him. Even that particular cue for him to give her his name went over his head, eliciting no response from him.

If she wanted his name, she would've asked for it. She didn't, so he assumed she didn't want it, and thus didn't give it. He had more questions for her, but he needed to hear her answer first, so he didn't ask them yet, remaining silent.

It likely came across as cold and rude, but most of the people around him were used to him being... him. He sometimes forgets that not everyone can translate Setsuna to English so easily.

If anything, her expression was easier to understand than the point she was trying to make. He wasn't trying to force answers out of her, per se, though there were things he did want to know. His expression changed slightly, shifting into a more patient look, but still with that sense that he could see right through any facade she could put up. He was basically waiting now, for her to give him those answers.

And he could wait all day, because he had nothing better to do. And he knew that she didn't either.