you set the iphone name in kind of a weird place on your iphone... go to settings... general... about. Then click on Name, and change it. It is weird since there is nothing else you can set in this screen. As far as it being your actual name "forever" maybe but not likely. The iPhone likes to reset this name every time it is restored, or even if you reset network settings. I have no idea why but it is not a very stable setting, it likes to revert back.
Then delete the phone from the car, and go into bluetooth on the phone and "forget this device" --the CRV handsfree link--- finally re-add it, new name will appear.