Domain registration
 

I have a question is their a way where I can register a domain without paying for it. I am currently using ip forwarding, but have somone who want to use my webserver to host their site so that is why I was wondering. And also instead of displaying the ip address display the host name like yourname.com. Thanks

Not unless you use a service like dyndns.com. If you wish to host a TLD on your site you will have to pay for it.

There are sites that offer free domain names, but they aren't going to be be "proper" domain names like you are looking for. They would be subdomains, like "yoursite.freedomains.com".