You have a couple of choices:
1) leave it registered under your Dad's name and account (If you purchase books you have to pay dad back
) and register your computer under his name (along with installing the software on your computer).
2) deregister the Reader and computer and then reregister the Reader and computer under your name (along with installing the software on your computer).
Option 2 means that you will have used up 4 of the first time period of ADE (Adobe Digital Editions) 6 device limit. It also means that you will lose the ability to read the book already purchased under your dad's name on your newly registered to you Reader.
I think that is right from all the posts I've read about this problem. I have my computer registered and keep my mom's Reader registered to my account so we can share books.