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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 mean, Vader still regularly recollected the memories of his past, but he 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:

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.