The StarCraft II Website announces that in conjunction with their new BattleTag system, Blizzard is offering free name changes in the real-time strategy sequel:

With the introduction of the BattleTag system, we’re in the process of evaluating how they might be integrated into StarCraft II, and how they may impact character names in the future. Instead of making everyone wait until we know how that integration could affect a name change system, we’ve decided to provide an additional free character name change for StarCraft II players eager to pick something else. We appreciate everyone’s continued patience and look forward to sharing more information on the future of the StarCraft II service as it becomes available.

If you'd like to change your character name, log in to Account Management and choose your StarCraft II: Wings of Liberty game license. On your game license screen a "Character Name Change" button at the bottom will initiate the request. After confirming that you'd like to change your character name, simply log in to StarCraft II and you'll be prompted to select a new one.