Not sure if I follow you, but Yes, it is possible to buy a domain name and web hosting separately from 2 different companies.

For domain name purchases you can use companies like:
GoDaddy.com
NameCheap.com

For paid web hosting, I suggest searching Google for:
"affordable web hosting" or "cheap web hosting", or screen our Shared Hosting Special Offers forum at HostingDiscussion.com

For free web hosting, I suggest searching Google for:
"free web hosting". In most cases, it will be ad-supported (thus your pages will display advertising).

Each hosting company provides you with their own nameservers that look like this: NS1.COMPANYNAME.COM and NS2.COMPANYNAME.COM. All you can do is log-into your domain registrar and edit the Nameservers to those provided by your hosting company. On average, it takes 24-48 hours for the domain to become active.

Best,