The bad news: It's gonna cost you $13.45 in cash money. Yes, despite many other online services allowing for free and easy name changes, Blizzard have announced today that they're only going to bother with the latter.
Anyone stuck with a BattleTag they came up with when they were 12/drunk and wants a change can head here to get the process started.
The company has previously offered one-time changes (and maintains its long-running offer of letting everyone change their name once for free), but this is a proper system now for changing it over and over again whenever you want. Provided you part with the cash, of course.
Note that if you do change it, the only thing it affects is your Battletag; everything else associated with your account, like your friends lists, remains the same.