I don't believe this is possible. In order to get <yournamehere>.com / .org / .whatever, you would need to register the domain name, which costs money. You would also need somewhere to serve the webpage from, again, costing... Your only free option (to my knowledge) is going to have to be through angelfire, or geocities, or whoever else does free hosting now....
I have my own webpage that I host from home, and I have a free dynamic DNS service, and it is <mysite>.no-ip.org .... but that again has their name in it, but it is a FREE option, if you can host it from home...