Vader should not be mentioned by name, but when Owen and Ben interact, Ben should make it clear that there is something worth hiding from, maybe vaguely referencing the Empire being a danger to Luke. Owen should even maybe guess/accuse that it's related to Anakin, while Kenobi insists that he's dead.
As far as the Son of Skywalker line, Vader (then Palpatine) learns the identity of the pilot who destroyed the Death Star a few months after the Battle of Yavin.
As far as the Son of Skywalker line, Vader (then Palpatine) learns the identity of the pilot who destroyed the Death Star a few months after the Battle of Yavin.