Does the Amiga know the IP address of the nameserver? Does the router perform this task for the other machines?
You have to enter an IP address for the "Name Server" entry before the Amiga will know whom to ask for the IP address of one of the other computers that you call by name only.
Frankly, I'd prefer to use fixed addresses on a network that is entirely under your control and where you don't have machines coming and going all day (like in an office with sales people connecting and disconnecting machines frequently). If you had fixed addresses, you would merely have a file "hosts" that lists all the machines on the network and their IP addresses. You would copy this file to each machine.
tony
PS: What is that person doing in your avatar? He/she appears to be sawing something, but what?