As mark was saying, Your Host (DH) does not have to be your register. I register my domains through network solutions, and host here. You don't ever have to use DH as your resitrar - just use yahoo and update the name servers to point here.
If you want to ditch Yahoo and move your domain registration here, you're going to have to pay that $15 or whatever. But this will simply add another year of registration onto what you allready have with yahoo - and leave DH in the mangement position.
Register= a company accreditated by ICANN to sell Domain names. .com .net .org .tv .whatever Registering a domain name, makes that name yours for as long as you pay for it. googlies.net will be mine for as long as I keep renewing with network solutions.
Host= a company who stores the files for your website. This Host probably also provides E-mail and other services for you and your website. You tell the registering company where you are hosting your files, and in 12-48 hours when anyone acorss the world types in your domain name they're pointed to your hosting company and your files there.
does that explain things a bit?