Few months off but I'm surprised nobody mentioned Diablo II.
Good one! Expansion was released in June 2001 so definitely counts.
Probably the game I've put most hours into of all.Not sure it's aged well though or would be as fun today.
Excellent game sadly only discovered it last year, still people online.It was a 2000 game, but the expansion was released in 2001, so I'm mentioning it here.
Rune.
Cracking bit of fun. Based on Norse mythology, it's a third person melee action game built with the Unreal Engine. How you moved when attacking with weapons, position of the weapon, etc, determined what attack was done and how it'd affect the enemy (dismemberment etc.) Anything dropped by a dead opponent can be used, so weapons, items such as torches, and yes, body parts. That you had just lopped off moments before.
Soldiers: Heroes of WW2. Released 2004, the very first in the Men of War series as it was later rechristened. An absolutely fantastic game.
Rechristened?
Soldiers: Heroes of->Faces of->Men of, that's what I would call a rechristening. Is that what you meant?