Does the 05 GXP have bluetooth in the entertainment system, or could there possibly be an after market radio system with bluetooth? Sounds like the previous owner set the system to link with his cell phone. If this is the case, you should be able to reprogram the system to turn bluetooth recognition off, or to recognize your cell phone (if your cell phone is bluetooth capable).
Of course, I could be completely wrong and one of the tech guys will chime in with a completely different response. My response is based more on knowing what some of the latest entertainment systems can do, rather than knowing what system is in your car.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)