If you have a cpanel, go into Parked Domains and add the new domain you want.
Go into your registrar's settings, and change the nameservers to hostgator's.
Wala! You've setup a new domain.
If you want to replace a domain on HostGator.com you have to contact there support and they should be able to support you from there.
To replace the domains hosting you will have to change the name severs on that domain to your new hosing name servers.
Open a support ticket on Host Gator and ask if they can change your main domain to the domain of your choice.
Change the DNS name servers and it should work.
Try adding a new Add-On domain in cPanel, this usually works. Or get HG to update your main account domain name.