@MolaCola No, there was no Tri Edge, and no killing of girlfriends. A Long time ago when I made this internet alter ego, I was playing through the 4 Original .(dot) HACK// games for the early PS2 (in chronological order: Infection, Mutation, Outbreak, and Quarantine), and at that point had not finished the games or known that Kite's legendary nickname would eventually become "Kite of the Azure Flame."
Because I did not know exactly what his legendary nickname would be, I combined the word "Azure" (because it was in both Balmung's and Orca's legendary nicknames, respectively: Balmung of the Azure Sky, and Orca of the Azure Sea ) and his player name "Kite" creating this internet alter ego, and getting fairly close to the idea of what his legendary nickname would become.
Circling back to the Tri Edge thing, not even the same set of games. And on top of that, Tri Edge never killed anyone, as far as I can recall in the entire .(DOT)HACK// universe nobody ever died, they only fell into a coma.
I mean hell, if you were to take a close look at My PFP then you would see the extreme lack of mismatched colors on the clothes, and that the Twin Blades he is holding are not in the G.U. series.
Personally, I couldn't exactly get invested into Blade Breaker, maybe because the chapters are +45 pages long? I don't know, it's only a guess.