I am pretty sure he means he can get to his website from a public location, using his ip address in lieu of a domain name.
All you need to do if you have that part working is go to a website that sells domain names such as Godaddy or Network Solutions, purchase the domain name and have their dns servers point to your static ip address.
If budget is an issue, there are places where you can register a free domain name, e.g. noip and dyndns.
I have a couple of domain names registered there (see my sig): the DNS hosts point my domain name at my public IP address, my router points incoming requests to the machine on which I run apache (website) and postfix (email).
When you're using an IP address, you're not using a domain. That's the point of a domain: it gives you an easy-to-remember name that you can use to reach a machine over a network without having to remember its IP address.
I think the word 'domain' is confusing the issue.
Do you want to host a group of web sites with a custom last three letters such as www.mysite.grt?
You can not make up your own top level domain (TLD) It is a HUGE deal to get one approved. I doubt anyone on this forum could get a new tld approved.
There are other uses of the word domain, if you mean one of the other uses, please clarify your question.