Blizzard have revealed
StarCraft II players can now log into their account and change their character name. But you only get one.
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. Please be sure to use this name change wisely.
Not sure why anyone would want to change their name after having already made one up, but each to their own.