“Hello. I haven’t seen you around school, are you new…?” she asks, but it sounded more like she was asking the question to herself more than you

She spaces out for a second, then shakes herself back to the conversation “O-oh, I’m sorry, I forgot to introduce myself, my name is Yuri, I’m a member of the literature club. What’s your name?” she decides to go with a classic, formal greeting, not wanting to come off as anything unnatural or weird.