If Kylo doesn't feel it fits him, then Vader isn't inclined to ask him what it was. He spends too much time protesting Anakin Skywalker is dead to be a hypocrite about it. But then, he was also aware of Naboo's culture.

He reacted up, taking Kylo's face in both of his hands. "My wife, yes she was my wife, we married in secret because we had to, was from Naboo. They are generally a wonderful people. Respectful. They have a tradition there, of changing your name if yours no longer fits, if you grow beyond it, or if you simply must cut ties with your past. She changed hers, and most of her most loyal changed theirs to match her's to honor her. Did you know that about your grandmother?" Probably the most shocking thing about Vader was how his voice softened, gentled, when he spoke of Padmé.