"Internet nexus of cultural Judaism" — Examiner.com
So, Dunham said that two of the four main characters are Jewish. Shoshanna clearly is, Marnie clearly is not. Jessa and Shoshanna are cousins, so Jessa could be part Jewish. But Hannah herself is the obvious choice.
The non-Jewish sounding "Dunham" last name is the last name of her non-Jewish father (she was raised Jewish though)