I don't know anything about mototrbo radio software. But I know about puting a server on internet.
When you have a server on internet, you need to have a way to find it. An static IP address is one of the ways, however for small applications is better having a domain name because an static IP will cost you money and maybe your ISP have to change the actual internet configuration on the router.
If your internet connection uses dynamic IP addresses (addresses that change periodically) then you can get a domain name on http://www.no-ip.org and use that name to connect from the remote site. They have free domain names and also prepaid plans.
On the router that connects the server to Internet you have to configure a port-forwarding because each server on internet have one or more ports (imagine they are doors) open.
Web servers usually open port 80 (http) and email servers use some (25 and 110, for example). The port is the conduit to let pass only the kind of traffic that the server knows to manage.
Supposing your server uses port 1080, you will need to enable the port forwarding of port 1080 from internet to your server and it will let your server be accesible from internet. Combine this with the domain name and you have it.