Ok. Yes Anakin Skywalker became Darth Vader, the most ruthless and feared villain in cinematic history (at least when ANH first opened). Yes, he brutally murdered fellow Jedi including innocent younglings who couldn't really defend themselves against him. Yes, he took part in many brutal acts of the Empire including destroying the entire planet Alderaan. Yes, he tried to kill his brother, mentor, master and fellow Jedi Obi-Wan.

But did he truly ever become Darth Vader?

I think when he lost his battle on Mustafar and the Emperor transformed him into the half man/half machine Vader we all know, he did give into that side of himself. Especially after Sidious told him that he killed his own wife. But he always took with him his fear. His fear of the Emperor being displeased with him and finding a new apprentice (another fear of loss). It was Anakin's fear, not Vader's. He manisfested this fear into power and intimidation, going as far as killing his own men for failing him or their mission and allowing that fear to hang over his subordinates heads.

Then when Sidious told him about the Son of Skywalker coming into greater power in ESB, it rekindled some old feelings. Vader as Anakin, knew it was his son. He even told Luke in their battle of Bespin that Luke was his son. Would Vader have told Luke he was his father? I think not. If he truly had given himself over to Vader he wouldn't have so readily admitted to being Luke's father. It would have been a much more cut and dry submit or die battle, and less on the emotional side. He even went as far as to tell Luke they could rule the Galaxy together (after overthrowing the Emperor). These are the words of a thinking person underneath all that armour and a person who doesn't want to really lose his only son. Another loss chocked up for him, one in which deep down he really didn't want to suffer. After all at the end of ROTJ, he tells Luke "tell your sister you were right". He is of course referring to the fact that Luke was right that there was good left in him and they both knew it. When he realized that Luke had, in fact, saved Anakin he could truly be at peace, and thus hurled Sidious down the reactor shaft.

In all, Anakin never was truly ruled by Darth Vader. He submitted to his new identity for a while letting his fear of loss continue to rule his actions, but in the end, he revealed that Anakin was there all along.