First, Uko's last name "Uumoto" uses kanji for rabbit "兎" twice ("々" is used for kanji repetition), that's why Nori-chan said it's very "rabbit-like".
Second, Like Hane-chan said, sometimes there are many reading for a kanji so a family name can have the same kanji and could be read differently.(You can see that there is even a specific book to teach you how to read Japanese last names)
It's not much of a joke, it's just that they did a blunder and read Nori-chan's last name wrong.(because they[Hane] are afraid of being find out of being the rabbit people)