Answer

He means to say that this is a family whose actual name is that, as opposed to “Beit Hillel,” which is a group of Hillel’s disciples, or “Beit Chonyo,” which is the name of a place/house that Chonyo established (and there is the well-known dispute between Tosafot and the Ritva regarding someone who divorces a woman on condition that she never enter her father’s house, and then the house collapses—whether the new house her father builds is included in the prohibition or not, and whether this is comparable to vows or not).
How does he know? From wherever he draws all his explanations of the Talmud—from his understanding of the text itself or from tradition.