There are two alternatives to the DNS: /etc/hosts and
NIS (Network Information System). /etc/hosts may be
used on simple networks. You must manually synchronize all
/etc/hosts files on each machine on the network.
NIS is a good alternative. It goes further than the DNS as it also manages user accounts and passwords. It can be used at the same time as the DNS (See "search path for host name" in the "Network configurator" menu).
Given that Linuxconf does not manage NIS servers yet, setting a DNS on your network and pointing all machines to it is a good idea. It is also a good idea because at some future date, you will connect your network to the Internet (with or without an intervening firewall). Then, you will need to point to a DNS server anyway. Yours will be just fine.