You can keep your domain registration separate from your hosting and I usually suggest that you do, allowing you to remain in control of your domain name. Nearly all domain registrars provide a login username and password so that you can sign in to your domain name manager. Your domain name manager will allow you to point the domain name to any server that is hosting your web site, as well as provide many other services related to domain name management.
If the hosting entity controls your domain name, you will some day sweat bullets if your business relationship goes down the tubes with the hosting company. Many hosting services will register your domain name in their company name, although they should be registering it in your own name.
I register many domain names for my clients simply because they don't want the hassle of doing it themselves, and I use Godaddy. I chose Godaddy because of their superior domain registration administration panel which easily allows me to add new domain names, renew them, register domain names anonymously (private registration), set auto forwarding of multiple domain names to a single domain, park them, or sell a domain name if I no longer want it.
I normally recommend that my clients signup at Godaddy so they can learn how to control and manage their own domain name. Signing up for the Godaddy service doesn't mean you have to host your web site with them, and hosting with Godaddy doesn't mean you need to register your domain name through them.
I've used other domain name registration services but after being burned by companies selling out to other companies and suddenly being charged for services such as pointing multiple domain names to a single domain (which should be free), I've consolidated my entire domain portfolio under Godaddy and have never looked back. They provide excellent customer service and the signup process takes only seconds. The end result is that you can easily login to buy new domain names or use the other domain name management services that they offer.
Be especially careful of Godaddy affiliates because I find them for the most part to be unreliable. Affiliates have the same Godaddy interface but do not carry the Godaddy name. Affiliates will come and go and they will likely try to charge you for services that should be free simply because they don't do the volume of business necessary to keep their prices low.