Let's say that we're testing a webserver where the pages served depended on a domain that you don't own. The most common way I know to test this is to modify your
/etc/hosts file to contain the hostname and ip address you want to map it to.
I've recently discovered that the command line utility
curl has a quick and easy option to forge the hostname of a request.
curl --resolve domain:port:ipaddr url
There are also browser extensions that you can use such as LiveHosts to get around this as well. This post isn't entirely useful when talking about permanent services.
If this is going to be a publicly facing service, then you should just set the records of your domain name to point to the server.
If it's a non-public routable service, then perhaps try looking into setting up your own private dns server.