In the comics I'm not sure that women, on Krypton, have their house as part of their name like the men do.
I mean, you have Kal El, Jor El, Jax Ur, and so on. But Kal El's mother was Lara, not La Ra, and his cousin was generally designated as Kara Zor El. This indicated a very patriarcal society that defines women by the name of their fathers rather than by their house.
Just a thought.
Tank (who has never been impressed with Krypton as a society)
