The name on the account is the only part that has to match - not the billing, the address, etc.
Most likely you helped your gf set up her account, and your name was on it originally? If it transferred, for some reason the same name is on the account.
The billing info doesn't matter - the registered name is what they check, and it is checked by computer. If you attempt to transfer with a last name even one letter off it simply won't even start the transfer. It gives a message that the destination account is ineligible.

On the purchasing part... you can upgrade in account management without buying the box game, but unless you are outside the US, buying the game in store will be about $10 cheaper. I'd look for the battlechest with WoW and BC (and of course use refer a friend on yourself).