If this is strictly a peer-to-peer LAN (vs. Domain) then the only only mechanism in place for name resolution is NetBIOS. In order for that to work, NetBIOS over TCP/IP has to be enabled in the network connection properties. Also, the default XP/2000 setting is usually "obtain NetBIOS settings from DHCP Server". If you're using DHCP from a router, it provides very little in setting info that is usable for resolution beyond gateway and DNS info. If this is your scenario, or you're using static IPs, try setting to "enable NetBIOS over TCP/IP".
What are the client operating systems being used? If any 9.x clients, it get even more colorful, as we now need to look at bindings.
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