I didn't think this was possible, but mIRC can get the name of a network, even if it is not specified by the user in the server list. I tried using a packet sniffer to see if perhaps there was a message sent on connect that sends the network's name, but I didn't see anything.
The network name is needed to display to the user as well as determine if multiple servers are part of the same network. I'm hoping this is a problem someone else has already solved.