[Hux didn't argue with Anakin. He was fairly certain that Padme remained dead but he would let Kylo Ren tackle that subject. He didn't flinch as things started to shake, Kylo Ren had done far worse around him already and Anakin needed him for information.]

The Imperial records have no mention of either of them. No one, not even the Emperor, knew they survived except a few. They were hidden- Leia was raised on Alderaan with the Organas and Luke grew up on Tatooine.

She became a senator on behalf of Alderaan until the Senate was dissolved and Luke- well I don't know what he did before Yavin.