Step 1 - Login to Your Billing Account
Your billing account is different than your normal web hosting control panel account. You can access the billing page at the following link:
http://gbclient.hostgator.com/login, which was also included in the account information email you got after signing up.
You'll then be asked for your billing account email and password. As mentioned before, the billing password is different than your normal control panel password, and it's also mentioned at the top of the account information email.
Step 2 - Go to View Hosting Packages
Once you're logged in, you'll see the Hosting Packages section in the bottom-left part of the page.
Click the View Hosting Packages option.
Step 3 - Click Change My Domain
You should now see an option called Change My Domain. Once you click that option, you'll be asked for your new domain name.
This was taken from
http://www.masterslair.com/how-to-change-your-hostgator-primary-domain-name if you visit the page it has pictures and things to show you how to do this. It is really simple.