Hey Krinkle. I had the same problem when I made my 5th account. I used my Visa card for the first 3 extra accounts but
had this same problem when i made my 4th extra account (5 in total).

They where all under my name too. Believe me, I spent days with blizzard billing support and didn't have any success. They are completelly useless.
What I did to fix the problem was to just buy a retail copy of the game and use the code. It woked first go and had zero problems with it.

It must be a security measure but I'm not sure.

Hope this helps.

-theforumlurker