Can you rename ethernet connection (not talking about WiFi)

Can you change the network name you connect to if you use an ethernet connection? WiFi is already renamed something like 'MyWiFi' but when connecting directly with an ethernet cable the network is the default network name. So, if I connect via WiFi I get connected to 'MyWiFi' but if I turn off WiFi and use ethernet I connect to XFSETUP which is the default network name on the bottom of the gateway.