Ok Not too sure about domains.

I need help. This is probly one of the dumbest questions… but please
spare the laughs. I want to create a domain controller. Like
RunMyServer.com. I know how to create it on my server… I think. However
how do I make sure that it is registered on the internet? I mean if my
computer is logged onto the internet 24 hours a day how do I have it search
the internet to make sure the domain is accurate? I can register a domain
name but it requires a name server.

I tried this before and I never could get the server to start correctly
because my domain was not registered on the internet. If I am a small
company, do i need 2 Domain Name servers? Help… Any advise?

Sorry… Just learning about W2K. Thanks