You don't have to use bind - though it is an option...
I just register my domain then in my DNS settings point it to my IP address.
If you have a dynamic IP address, then companies like easydns.com offer dynamic updating of your IP - you run a little client program that monitors your IP, checks about every 10 min or so - when it changes it automatically notifies your DNS provider and updates the info
easydns.com is $35/year if you want to use the dynamic IP updating.
If you don't need that service (either static IP or it changes so little that manually updating it wont' be an issue) then any domain register that gives you control over the DNS zone fields will work... I use namealerts.com ($8.95 registration fee for domains).
I currently do this with my game server - configured the dns info for cssquad.net to forward to my game server IP - you go to it and you would never know it was being forwarded
(game server has static IP)
Seems to me if your running bind, you still need a domain pointing to your computer so that it can resolve correctly - how else will the other DNS servers know where your DNS server is to resolve your domain name?