You can register your domain name through one hosting company and you will be able to point it to any web hosting company that you choose. You will always have access to your domain manager, and will be able to modify your domain name records any time you need. Thats the great advantage!

Everything depends on your choice. You can host as well register a domain with same company there is no harm in it. In the same way you can also choose different company to host & register a domain.