Try doing a /names q~#channel.
I am assuming the channel name is the same for both channels. The results should come back #channel and not q~#channel so mIRC does not know the proper target for the updated names. Mostly this is a flaw with the BNC.
mIRC does support multiple servers/connections so you might want to up your BNC to allow two client connections and connect to it twice from mIRC. Then the client will properly handle all the different networks, channels, queries etc.