There are some models that have more advanced functions but looking at the default wireless extender, you can not create a private network just for you.
The extender works by simply taking the signal and rebroadcasting it.
If there is no settings in the extender to set a different SSID and password then it cant be done with the extender.
You will be better off getting an av1000 or faster powerline adapter. Then you will have a faster conection and control what gets plugged into it.
Note this will not make your connection the priority at the router, you will need to configure QoS settings (if router even has that ability).