If Vader didn't know about Shmi 's claim that he "had no father" then he could have concluded that the Skywalker was a more distant relative. In the book, there's a detailed passage showing Vader's thoughts on the subject: Even while inspecting his nearly completed flagship, the Super Star Destroyer Executor, at the Starship Yards of Fondor, Vader could not get Luke Skywalker out of his mind. He silently chewed on the name, and considered the fact that the boy had been born three years after the death of Shmi Skywalker. To the best of his knowledge, Anakin Skywalker had been his mother's only living blood relative. Could there have been other Skywalkers from Tatooine? Vader allowed the possibility. After all, it wasn't an entirely uncommon name in the galaxy. But Anakin and Padme Amidala had been expecting a baby nineteen years ago. Nineteen standard years. It's not possible, Vader thought. I killed Padme. The baby died with her. Not for the first time, he wondered if the Emperor had told him the whole truth about Padme's death. But I remember choking her ... seeing her collapse on Mustafar. I was so angry with her. And yet ... Luke Skywalker exists. Vader refused to believe the notorious Rebel's surname was merely a bizarre coincidence. If he had possessed any other name, Vader would not have hesitated to report what he had learned to the Emperor. But for purely selfish reasons, Vader kept the young Rebel's name to himself. To him, Luke Skywalker was more than a mystery to be solved. He is ... an opportunity. As strong with the Force as he may be, he is an opportunity ... an opportunity for even greater power. But who is he? Who were his parents? Could he have been Obi-Wan's son? But then why was he named Skywalker and raised by the Lars family? Or was he merely trained by Obi-Wan? Because Obi-Wan Kenobi, Shmi Skywalker, Owen and Beru Lars, and Padme Amidala were dead, there was only one way Vader could discover the truth. He would have to ask Luke Skywalker himself. All he had to do was find him.