well, the public domain name you purchased will only work for things connecting from the public internet. for within your network (lan), you will need to configure your local DNS server to know where your openfire server is located. If you have a standalone DNS server, you probably already know how to configure it… just add an A Record which has your Openfire server’s FQDN and points to it’s IP address. If you are using DNS through your router, then log into it, and usually there’s a DNS config area where you can setup host names and IP addresses (the same thing as setting up A Records and Pointers but just through the router’s webui). This way, when your PC looks on your network for your openfire server, it will ask the local DNS server first (your router or standalone dns), which will respond with the openfire server’s ip address.
for public access from the internet… you will need to setup your new domain name to point to your public ip address (hopefully you have a static ip address). Then at your firewall/router, allow the necessary ports through to connect to your internal openfire server. This is usually done via NAT. To see which ports you need, log into your openfire admin ui page, and on the main page, at the bottom it says “Server Ports”. Make sure at least you have port 5222 open through your firewall/router. The rest of the ports are up to you… but could pose a security problem (ie. if you allow your admin ui page to be opened by anyone on the public internet… so perhaps don’t open all those ports unless you need them).