I suggest you read up on /etc/hosts and how to give your system a name before you set up yourself as a nameserver. Another thing that you need to look at is the hostname. Running hostname from the commandline with the right switches will tell you what name your system thinks it is, and will let you set that name also. Just man hostname.
And finally you will need to use register.com to tell it what names your system answers to. If you only have 1 system you can do *.yourdomain.com. But I'd suggest you just let your system be listed on register.coms name servers.