For internal zones, the easiest is probably to edit and add to your /etc/hosts file and enter your hosts in the format :
IP DOMAINNAME ALIAS
192.168.0.10 server1.example.com server1
192.168.0.11 server2.example.com server2
192.168.0.1X server3.example.com server3
( don't change the localhost settings unless you know what you are doing
copy this file to each computer, and away you go. You should be able to ping or ssh each computer just using the ALIAS instead of the IP.
the more challenging thing to do is setup BIND, which is probably overkill for you.
Good luck !
ps you may want to backup or copy the file before you edit anything. Just in case. You need to edit using SUDO.