No way really. I mean it depends how you did it. You will have to do some convincing. You can't just call up blizzard and say hey I forgot my last name.
You will also need email. When using the posing as a company scam, I usually say that I need to verify the last name with the paypal account. They will usually use the paypal account that they own and it will tell you the last name. Beyond that you can't really get it unless you can convince them to. Good luck!