You can do it actually, but it is a hell of a process. I had two accounts, both in my name but one was for my ex wife. After we divorced, we had contacted Blizzard about getting one of the accounts into her name. It was a long process. Involving multiple phone calls to and from Blizzard, photocopying identification documents like drivers license etc to send to blizzard, written letters from both us yada yada. Honestly it was more damn trouble than it was worth.
They made it very difficult and in the situation of the OP, seriously, I wouldn't bother. Blizz can do it, but they're very particular about the reasons why they'll allow it. My process took almost two months from start to end. You can call/email blizzard ask them, but for your situation I very much doubt they'd let you.