If you mean initiating connections from one computer on your local network to another, you need to install and enable avahi-daemon (or some other mDNS daemon) on the “fancy” one. Your router also needs to support and enable mDNS forwarding, but basically all of them do by default. Then just use your-hostname.local in place of the local IP address, and your computer will automatically resolve it using mDNS. It’s different than regular DNS, so it doesn’t need any special configuration to use it. And word to the wise: don’t use uppercase or special characters in your hostname.