How to sense mobile signal coming to a room using arduino uno
You can't.

Mobile phone signals don't respect artificial boundaries like a room's walls.  You can detect the mobile phone signal from the local cell, but you can't narrow it down to "what is talking to a device in this room".

And if you could just intercept the signals and find out who was calling whom there wouldn't be much security, would there? It's all encrypted and locked down - you can't get at that sort of information "from the air".

What you could do though, is to have your mobile phone send out the phone number of an incoming call via bluetooth (many hands free kits already use this kind of facility) and have your Arduino receive that information to display it.