I have been called an odd immortal lover,
or even worse Dill doormat mover,
But I answer none of those.
You may know two of my other names,
One I have rejected and one I have become
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You were born as:
Tom Marvolo Riddle
But spurned this name by:
Anagramming it to I AM LORD VOLDEMORT (since you wished not to be known by the dirty muggle names of your ancestors). Both of the two other phrases in bold in the question are anagrams of the same letters. And in case anyone is in any doubt as to who you are, you are the main antagonist in the Harry Potter franchise!