actually, the answer is yes, fsgames, although DPS is also correct.
What DPS is saying is that if you want a genuine www. domain, recognised by ICAAN and accessible to anyone with a World Wide Web-standard browser, then you have to use a ICAAN-registered registrar who will purchase and administer the domain in your name.
However, with some fairly cheap software and a little programming, you could choose to have any domain you wished, including the best (most expensive) in the world, like business.com, ***.com or even -gulp- google.com! The only thing here is that you would need a server at home to run the portal and you and anyone who wished to access your version of, say, google.com would need to have a copy of your specially-created browser.
This is pretty much exactly what the much-advertsied dotworlds.com is doing currently, but you could make the basics fairly easily with the software and a server. It wouldn't work with Firefox or IE, of course, and it wouldn't be a recognised domain, nor could you send emails from "@google.com" but you would still have a domain that other people with the software could access (if you designed a
website hosting).
Hope this makes sense.