How do I host a site with outside registration?

Hi, I’m currently hosting a site under a domain name which I purchased through my account with Dreamhost. However, I would like to transfer this domain to a GoDaddy account so that the billing is done through there, and not my Dreamhost account. Is it possible to host a site without having the registration under my Dreamhost account? If so, do I have to upload the files to a separate domain name and the original domain name redirect to the separate name or what?

Yes - at the place you register the domain (and pay for it) set the nameservers for the domain to