Any web host can register domain names for you if it has not been purchased any where else. The cost is anywhere from 8 to 25 USD for 1 year and 15+USD for 2 years. Excluding any existing free domain name special which may be happening, in which case your domain name that you have chosen to use, will be free if it is a new one and not yet registered.
If you already own a domain name you will need to modify the DNS settings where you purchased the name. You will need the following information below.
The host name and dns information will look like this below: