Well I'm no expert, but I do have a domain name pointing to my PC. Mine is http://www.dootdootdoodydoodydootdoodoooo.com/ I just bought my domain name from Network Solutions.com and then said to point the name to by IP address which is a standard domestic ADSL connection.
You can be accessed by your IP address and you do not need a domain name. People will just have to type the IP address in their address bar instead of a name. But you can't use dns without a domain name because that's what it is, Domain Name Service.
In order for a domain name to be officially accepted by the severs of the world, which is what you need or no one can ever be pointed to your server, it must be officially registed with ICANN. You have to be a registrar in order to do this. Not just anyone can become a registrar either. First and foremost it takes bundles of cash, secondly you have to be approved.
Once your domain is registered though it is propagated throughout the world-wide network and stored on various special servers located throughout the world. These servers basically store the information as to where to point someone looking for your domain name.
You can however make your own domain name to use within your own intranet. You would need to create the files that tell the other computers where that domain is located though. It is the same principal as above except on a much smaller scale.