I am looking for a solution to this as well. Did you find one?
As far as I can tell, Windows only sets a "custom name" for wireless connections using the SSID name. it will use "Network #" for wired connections unless you have connected to a wireless network first that uses the same Gateway MAC address and offers the same option 15 domain name...which is probably how you got your KITLV_STAFF_FREE name to show up for the wired connection instead of "Network 2".
The only other way I have found to change it is by editing the registry keys on each PC, or pushing a profile via Intune or a DC.