my-ip must hold an ip-address of a network interface present on the system your eggdrop is running. If you're running it on a system behind a NAT-router, you'll have to use the internal address. If, on the other hand, your system acts as the NAT itself, you should be able to use any external ip used by the system.
Setting my-hostname is just another way of setting my-ip, without having to lookup the ip first. The same restictions apply here aswell.

In the scenario where your system resides behind a NAT-router, you'll have to reconfigure your router to use a different IP on any outbound connection from this system. Information wether your router is capable of this, and how it is done should be available in the documentation of the router.