For making website domain name is very important.Without domain name you cannot identify the website easily.
A domain name is the name of a site (i.e. Neopets.com or sitnamehere.co.nr) and some are free but others cost money.If you want to use a .com thing it will cost money,but you can get a free .co.nr site at freedomain.co.nr . You can also get one at freewebs.com but it's not really a domain it's subdomain name with free hosting .But paid domain name is professional for every business or personal site.You can register domain name minimum 1 year and maximum 10 years.To register domain name you can visit the site 9CubeHosting.Com
here you can first check availability for name which you want to register.If the domain name is available you can register it.If the domain name is not available for registration,you can register with alternative extension with same name or with alternative name with same extension.You can check domain name owner details at Whoisxy.com