Here's a thread that describes a very similar situation.

The key post here, perhaps is:

A clearly fake name "i.e. 'Mickey Mouse'" is POSSIBLE to change -- but realize that you signed the terms of use/eula saying that you would provide accurate information and you did not.

It's up to Blizzard if they are going to be nice enough to allow you a second chance on your current accounts. If not, you're out of luck -- buy new accounts. If so... well thank Blizzard for being so forgiving.

I'd say try it -- report yourself for having a fake name on the account and see how far you can get.