This might just be a "name" thing. I am not sure how windows chooses the name for a network. The part that matters is what is the IP address. The only way it will work cabled to the router is if it is in the same subnet as the router and has the router as the gateway. That really is all that matters what name you call that network is hard to say. I know sometime windows will use the wifi name for a network even though you are connected via ethernet.
Ping the router IP. On a ethernet you should get 1ms or maybe up to 3ms but it should be very constant. Wifi you will get much more and it will have random large spikes.