You should always be listed as the billing and administrator of your domain! Your host provider is ONLY your technical contact.
My experience trying to move a client's web site has not been good when dealing with ISPs who provide domain registration services and then control the domain by means of being the sole contact. Unless you are billed directly by InterNic you also have no receipt to verify your domain registration information.
It is understandable to charge an initial fee to register your domain, as this is time consuming and involves a verification process. But there is no reason for anyone to get paid to renew your registration when InterNic will bill you directly. When they control your domain you will have a very difficult time if you decide to change host providers.
Please protect yourself from services that register domain names and do not list you as the contact for YOUR domain. When a change is necessary it must be initiated and approved by the administrator or billing contact. If you are not listed as either or both, you have no control over Your domain name.
Read carefully when you sign up for Free Hosting as there are several now who state that they WILL and DO retain complete control of your domain name. Makes you wonder why you are paying for the domain name that they then will retain if you move from their server!
Great Resources:
Domain Name Buyers' Guide & Domain Name Buying Tips
Before registering your domain name visit the Registrar Rankings at: Registrar Rankings