Tons of people know nothing about the internet, nor the difference between registering a domain and then hosting.
Most hosts will offer domain registration but its so very simple to do on your own (and in about 5 minutes time) that we usually try to direct our pre-clients to do it themselves. With a few emails they have it done and didnt realize just how easy it would be. We do offer registration because we sell hosting and some people want that convenience of being charged one time for it all. In other words we offer it as a convenience.
I always suggest godaddy.com or 000domains.com for registration.
You simply register your domain name, and if you already know your hosts DNS then you can add that right into your domain record when you register the name.
It can be VERY overwhelming looking for hosting nowdays so please do your best to research any co. on your list. Be sure to send them some pre-sales emails BEFORE signing up anywhere.
Best of luck...you'll be a pro in no time :-))