[Yeah she's definitely mistaking her for someone else. Not that she didn't come to that conclusion before but this just makes it more obvious.]

It is customary and polite in Japan to refer to one by their last name unless the relationship can be deemed to be more than acquaintances or unless permitted to refer to another by their first name. [She puts her hand on her hip and shifts her weight to one leg] As we have never met, we are not acquaintances and we have not permitted one another anything.