During The Empire Strikes Back, Palpatine refers to the father of Luke as Anakin.
Darth Vader: What is thy bidding, my master?
Emperor: There is a great disturbance in the Force.
Darth Vader: I have felt it.
Emperor: We have a new enemy, the young Rebel who destroyed the Death Star. I have no doubt this boy is the offspring of Anakin Skywalker.
Darth Vader: How is that possible?
Emperor: Search your feelings, Lord Vader. You will know it to be true. He could destroy us.
Darth Vader: He's just a boy. Obi-Wan can no longer help him.
Emperor: The Force is strong with him. The son of Skywalker must not become a Jedi.
Darth Vader: If he could be turned, he will become a powerful ally.
Emperor: Yes. He would be a great asset. Can it be done?
Darth Vader: He will join us or die, my master.
This seems a little odd, considering that:
Vader is Anakin.
I realise that to have said that too early in the film would have ruined the big reveal. Is there some in-universe reason for Palpatine to refer to Luke's father as Anakin? Some kind of psychological game that Palpatine is playing with Vader, perhaps?