Board Thread:Theories and Speculation/@comment-1512913-20161122142914/@comment-1512913-20161122221038

Most likely a female from the main family is a princess to the clan. Just like Kaguya was princess of Otsutsuki Clan, Hinata is also a princess of Hyuga Clan, the heiress, even though she gave up the position and it's Hanabi now. The Otsutsuki were able to sense how pure a Byakugan is, so they were likely able to tell that she has to be from the main family according to the pureness.