Depending on where your friends on (inside your network, outside your network) you may or may not have to register a domain name (or get a free one from somewhere like dyndns.org). If they are internal then it's as easy as getting a centralized DNS server (usually a router has one in it, you just have to figure out if you can manipulate it or need to disable it and let your Mandriva system do the DNS for your network) to resolve your hostname to your IP. Then (for any device who uses your DNS server as a DNS server which should be most if you setup your network right) all you have to do is what you've noted above.
If they are outside your network and you have to get a domain name registered, you would need to use port forwarding from your router (you do have a router right?) to point port 80 (the http port) to that machine; this is called Port Forwarding in a lot of routers but might be called something like Applications and Gaming depending on your router type. If you have no router or firewall then all you will need to do is setup your new domain to resolve to your IP (something like 242.17.144.5; not 192.168.1.X or 10.0.0.X).