Blizzard says NO

"Hello,

Thanks for the email. As we have explained in a previous email, detailing the account changes procedure, unfortunately the name of the account holder cannot be changed at all. It is for this reason that we don't mediate or facilitate in the transfer or sale of accounts, and thus any actions are done so at your own risk. You can still play without any problems but be aware that we will require the original owner name if you ask us to make future changes.

Should you have any further questions please don't hesitate to contact us again"