I found how to rename:
netsh interface set interface name="Old Name" newname="New Name"
or, with PowerShell:
Get-NetAdapter -Name "Old Name" | Rename-NetAdapter -NewName "New Name"
What I need is to set a name for an Ethernet card I do not know the name of. The reason I need this is that some computers I'm servicing remotely simply reset their IP configuration by themselves from time to time (this is what the clients claim) and I need to be able to set them back to a working configuration automatically. Upon fixing this issue, the script seems easy to build:
netsh interface ip set address "connection name"^ static 192.168.1.10 255.255.255.0 192.168.1.1 netsh interface ip add dns "connection name" 184.108.40.206 netsh interface ip add dns "connection name" 220.127.116.11 index=2