There is only one way to stop a device from registering on a router - don't connect to the router either by WiFi or Ethernet.
The router will show all connections. If you try and disguise your device, then your Dad will see a connection he does not recognise. He will probably change the WiFi pass phrase to lock out the unknown device, and then you will not have a WiFi connection.
Using a VPN will probably make him suspicious as to what you are doing anyway.
I hope this helps.