Check your real IP at
To make things easier, look for a free subdomain (for instance at freedns.afraid.org), install a dynamic DNS client updater (that will upload your actual IP to the DNS servers), ... and that's all.
If you can access your server using it's actual IP (the one that's displayed by the script above), you can access your server by it's chosen domain name.
You can check if your server is online from my site:
This home server runs on a dynamic IP, the only way you can tell it's not a 'regular' server is it's port number: 20800