Battle.net name.

Q u o t e:
In the case of a legal name change due to marriage, divorce, or the like, they will need copies of legal documentation in order to make that change.

For legal name changes you'll likely need to fill out a form and provide appropriate documentation, Pimar, though if you need to change the name because you made a small typo when creating the account they should be able to help as soon as you are able to verify specific account information.

Good luck!

o Website E-mail Form
http://www.blizzard.com/support/wowbilling/?id=eSupport000
o [email protected]