How do you register a Domain Name?
 

The thread title says it all.

register.com

I think I used GoDaddy. You can register a domain name for less than ten bucks.

I used GoDaddy as well.

So, the place I am purchasing web space from said to just register a new domain name, and they will set me up.

How do they know I registered that name? I guess I just don't understand the whole process.

Side note: I have webspace but I want to change the name of the web-address (I inherited this space and name, so to speak).

You need to find out the IP number of the server you want to change domain name to, then you enter that IP number in the registration process instead of settling for the default server (which they'd like you to purchase as well).

By the way, I've used godaddy.com too. Cheap and reliable.