Can you rename ethernet connection (not talking about WiFi)

Got a new modem and the network name is NOT the name I use/want it to be.  I am using a ethernet cable connected directly to the modem.     

Can you change the network name you connect to if you use an ethernet connection?

WiFi is already renamed to my preferred name and connections have been established.

but when connecting directly with an ethernet cable the network is the default network name.

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.