If you're still dissatisfied with your StarCraft II moniker, Blizzard is giving you a break. They're going to allow players to change their name once for no charge while they continue working on the BattleTag feature.
"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," said Blizzard. "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."
BattleTags are a social feature similar in concept to Real ID. By sharing your BattleTag with other players, you'll be able to chat with friends across different Blizzard games or form groups for playing. The main difference between Real ID and BattleTag is that the former requires you to reveal out your e-mail address and real name to other users. A BattleTag is a nickname picked by the user.
The chat features of BattleTags are currently live in Diablo III's beta. They'll be integrated into that game at launch as well. No word on when Blizzard intends to integrate BattleTags into SC2 or World of Warcraft.
To change your character name in SC2, log into Account Management at Battle.net. Then, select your StarCraft II: Wings of Liberty game license from the list of titles attached to your account. You'll then be taken to your SC2 page, which will have a "Character Name Change" button at the bottom.
This is the second free name change that Blizzard has offered to the SC2 community. The first was made available in late 2010. Thus, you've had over a year to think of a new "dirty but not reportable" name for yourself.