Actually, you need to register your domain name, then have your ISP add your new domain name in their DNS servers...
As for your IP address, I didn't see anyone mention static or dynamic IP addresses...
Static IP addresses always remain the same... Dynamic IP addresses can change...
Some ISP's create a permanent entry for your computer, on their bootp or dhcp servers... Others do not!
If you've been assigned a static IP address, you can enter all of the appropriate information in your local Networking TCP/IP properties GUI.
If your ISP is using DHCP or bootp to assign the IP addresses to your local machine, then you don't want to hardcode those entries locally...
If the ISP decides to change your IP address, and you have it hardcoded, you could conflict with whoever else has been assigned to this address... In the event of a TCP/IP conflict, it could lock up networking on both systems...
So... Check with your ISP... See whether they're using static or dynamic IP addresses...
Ask specifically for a static IP address, if possible, or ask them to modify their dhcpd.conf file to provide you with a permanent address...
Next, after you've registered your domain name, ask the ISP to enter the new name in their DNS servers...
Hope this helps...
Joe F.