When set to using DHCP, the IP address of the machine can change. When running a server that can be annoying so in the past, I've generally assigned it a static IP and edit all the other machines' /etc/hosts file to give a name that points to the server. Instead of keep doing this, I decided to have the Linux server broadcast its name to the local network.
Edit /etc/sysconfig/network-scripts/ifcfg-eth0 by adding DHCP_HOSTNAME=<your machine name here>.
This is the location for Fedora so your distribution might be different. ifcfg-eth0 is dependent on whatever network adaptor you want to config (i.e. if you're using a wireless adaptor it'll have a different name).
Finally, restart the network and your server should be found by your other machines simply by its name.