Vader's relationship with Anakin?

By the time of ANH had Vader dissolved all memories of his past as Anakin Skywalker, or was he still holding onto that fragment of himself on some level, maybe because of his love for Padme?

I don’t believe so, as said he thought she was dead.

There is the chance that he was doing it because he thought it was what she wanted, but I am not sure.

Most likely he did it because he actually believed that the Jedi were evil.

Check ROTS, battle with Obi-Won is where he stand that kind of stuff.

I mean, Vader still regularly recollected the memories of his past, but he [Vader] got to a point where he no longer thought of himself as ever having been Anakin Skywalker. As far as Vader was concerned, he and Anakin were two completely separate people -- he even referred to Anakin as "The Jedi"; never as himself.

Zahn confirmed this in an interview:

StarWars.com: Speaking of Anakin, Darth Vader has compartmentalized his own life, not even thinking of his past self as Anakin Skywalker, but as "The Jedi." What does this say about him?

Timothy Zahn: Vader doesn't even think of himself as once having been Anakin Skywalker. Those memories are somebody else's.

Different authors have different opinions. Lucas always thought that Vader considered himself as separate from Anakin. Most authors in Legends and in Canon have gone with that idea, but some have suggested that Vader did think of and miss his old life, on occasion.

I'd say both. He instinctively wished to be Anakin again but he knew that cannot be possible and had to bear the guilt in his soul of betraying his brothers in arms.