Breaking down MC and his desk mate's names:
MC: 女 (Suke) 蛮子 (Banji)
New Girl: 男 (Dan) 男子 (Otoko)
The reason other characters get them wrong is that all 4 names are extremely unusual (there's like 10 people in Japan with the surname 男) but 3 of the names are common words: 女 = Onna = woman, 男 = Otoko = man, 男子 = Danshi = man + child = boy.
Meanwhile, 蛮子 isn't a word or a name, but 子 (read "ko") is an extremely common end to a girl's name, to the point that you can tack it onto a lot of things to get a feminine name. Just not 男.
So Japanese people's first guess for the two names are gonna be "Onna Banko," and "Otoko Danshi," and they'll assume that Onna Banko is a girl and Otoko Danshi is a boy.