I have a 2013 Chevrolet Equinox and I recently upgraded from an iPhone 5. I gave my iPhone 4s to my girlfriend after I master reset it. My iPhone 4s was paired to my Equinox prior to the master reset.
Once I repaired my old iPhone 4s to the same car it still shows up as Matt's iPhone even though the new name is Elizabeth's iPhone. I checked to make sure the name is definitely Elizabeth's iPhone in multiple places. (Settings-General-About-Name) also on iTunes and when connecting to other Bluetooth devices.
Now, I tried deleting and re-pairing my phone off of the car's Bluetooth system as well as off of the iPhone 4s Bluetooth history. Everytime I repair from the beginning the car still shows up on the dashboard's computer screen: Matt's iPhone.
I don't know if anyone else has ever run into this problem or has any answers.
I also did extensive research to find a "Bluetooth reset" on my Equinox to no avail. I don't believe it exists.
I contemplated doing another master reset but the phone was just reset earlier today before trying to pair and not restored with the same settings.