Many hosting providers provide an opportunity to order hosting from them and register a domain name for free. As far as I understood they register domain for you and you are the owner of it. But what are the advantages of registering domains separately using services like GoDaddy, Name.com and so on?
if for some reason your hosting hacked and used for phishing /spam / abuse your hosting provider suspends your hosting and domains. its always good to keep domains in registrars than with hosting providers
If you need a full control on your domain, then it is always better to register separately through certified registrars. Hosting companies registers it for you, but if something happens or you have any issues regarding hosting, then you are screwed. See the TOS before opting for these free combo offers.
If you run into problems with your hosting provider and they registered your domain, some web hosting companies have been known to hold your domain hostage, which may take months to get it back if you are lucky. I would recommend any serious domain you desire to register it separately from your web hosting provider.
Buying a domain separately is good because companies like Godaddy, Name.com are globally known as a domain selling companies. If; in future you face problems with your hosting, then having a separate domain registration, you can transfer from your current hosting company to any hosting you like. BUT if the domain comes with a hosting company, then you would have to put your guts to get it back to transfer to another host. It might be an annoying thing to wait for months just to get your domain FREE... PS: If your looking for premium domains, do check my signature. Enjoy