router is able to display list of devices that are connected to the wifi,which could be a pc or mobile....but is it possible to hide our device from being displayed on the list
No cannot do this. Why would you want to do a thing like this?! The access to the router shold be restriced to a small number of people who are administrators. So why would you hide mac adresses?
Trying to hack WiFi routers? Sorry, not allowed to help you with that here... :-( If you are just looking for anonymous browsing, try Tor or other VPN services.