I'm not sure either what you mean, because all my machines at home have static hostnames, they don't change (I don't even know how that would be possible). I also have a DHCP router (D-link) which, in its default configuration, gave my machines a new IP every time I booted them up. It was easily fixed by turning on "MAC caching" in the router so that it will always give the same IP to the same MAC address (I needed it that way so I could run port forwarding to my FTP server). It was very easy to do in the router, you just selected the MAC address of a network card connected to the router in a dropdown box and typed in the last digits of the IP in a box.