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I seem to remember that you can delete the paired phone somewhere in the settings. I traded a Blackberry for an iPhone 5 and deleted the Blackberry info. That should delete the name as well.
I deleted the phones. In the navigation system I could rename my phone but my phone's (iPhone) Bluetooth device list show it as Barbara's GS. In my other car's it has typically said car multi-media.
Looks like its time for a name change. Barbara isn't such a bad name. I think there should also be a setting under the Bluetooth settings menu to change the car name if I'm not mistaken.