He also had one Marvel rebel give up the name via torture and another rebel flat sold him out over jealousy.
But Skywalker isn't an entirely uncommon name so he needed more confirmation.
One of the bigger mysteries of the original trilogy was how Vader found out so much about Luke Skywalker between ANH and empire. Marvel filled it in with a Boba Fett adventure.
The only one to do it in a very profound way was Randy Stradley’s Empire run for Dark Horse. He told the story of a “good” imperial officer named Janek Sunber. Sunber does the right thing and wants to make a difference. We see him navigating a collapsing system of corruption in the empire. Then the bomb drops. We have already heard of him. He is “Tank”, Luke’s friend who went to the academy with Biggs. We are given a reunion between the friends and then the break off between them.
Vader who is pursuing the Rebel who destroyed the Death Star finds out it is his son, but more than that. He finds out all about his son from one of his best friends. How he grew up, Owen and Beru, all of it.
The only two people that realize Luke is Vader’s son is Vader and the reader. The story of Janek Sunber is one of the best comic stories told in the Star Wars universe and worth the time if you find the issues.