Historians are pretty sure that the story contained in the Book of Esther is a work of fiction, and likely was always intended to be. So Haman, like most everyone else in the story, appears to be fictional. The only character that appears in it that is historical is Xerxes I (assuming that Artaxerxes is meant to be Xerxes), and his characterization seems likely fictionalized as well.
Berlin quotes a series of scholars who suggest that the author of Esther did not mean for the book to be considered as a historical writing, but intentionally wrote it to be a historical novella. The genre of novellas under which Esther falls was common during both the Persian and Hellenistic periods to which scholars have dated the book of Esther.
The point of the book simply wasn't to relate what we modern people would consider "historical accuracy". When it was written that concept didn't really even exist. It was intended to supply an enthralling origin story for the Jewish holiday of Purim. The ancients actually understood this well enough that they didn't have huge problems rewriting the story, which is why the Greek version is rather different than the Hebrew version. The Jewish tradition is even that their version is in fact a retelling of an earlier written version of the story.
Of course one of the things I always hasten to add when I have to say things like this is that just because the text we have isn't an accurate work of history doesn't mean its not important, both historically and morally. It can still be very good scripture. Some things are accurate, and some things are True, and they aren't always the same things.
For instance there's a story (perhaps apocryphal) that during WWII when things looked the most hopeless for the British they sent for a representative from the President to plead their case for how they could still win the war (and thus still merited US help). Roosevelt sent over his closest advisor, Harry Hopkins.
The story goes that after the British had made their case, they were waiting with baited breath for Hopkins' response. He stood up and recited from Ruth (1:16):
whither thou goest, I will go; and where thou lodgest, I will lodge: thy people shall be my people, and thy God my God.
Now did this actually happen? Likely not, since I've never been able to dig up a reference for this story since I first read it*. But its very instructive of what the relationship between those two nations was during that period of the war. So while this story may not be the best History, there's a Truth in it that would otherwise take a ton of dry instruction to impart.
Its also goes to show that this particular book was part of the mental vocabulary of people who were shaping history for the last 2,000+ years. The world without it may have ended up looking very different, and likely not for the better.
That's the kind of thing the Biblical authors were probably trying to do.
* - Well, I said this based on past failures to source this story, but lookee, it's sitting on Mr. Hopkins' WP page today with 2 references. Its a Purim Miracle!