I have cable TV and pay axtra for an HD DVR A friend is giving me another HD receiver to use with a second TV Can the cable company trace the receiver and know I have a second one?

No, you can not use that HD receiver because in order to start services on that HD receiver cable provider needs the Serial Number of that receiver and cable providers only activate services to their own properties they only can rent you their own receiver but can not activate the services on a box which is not their own