really? this seems bizarre to me! I used to work with the police (civilian investigator), and knowing how more and more prevalent digital evidence is becoming it seems mad that first point of call for a quick ID wouldn't be to check someone's phone. Swiping right to get to the ICE (doesn't need the phone to be unlocked) is so much faster than calling up control to search for a numberplate, then dispatching someone to address there might not even be anyone at.
It's really worrying you don't know that and assume you would need someone's PIN to access their emergency contact info - I was taught about it in a first aid class over a decade ago because lots of people also log their allergies, blood type etc there too.
Ignore the car reg aspect - imagine something happened to OP without her car being involved, how would you trace her then?
From my experience phone would be checked first, if no accessible contact info then bank cards or similar to get your name, or any other info - work lanyard, business card or something. Then put your name through police national computer to see if any record of you at all - even if just a witness or reported a crime years ago. Can also liaise with council to see if you pay council tax/receipt of any benefits etc - although obviously that's assuming the incident happens where you live, and can take some time. Hospitals can look you up to see if you are logged anywhere on their systems as a patient or NOK, but again, not as helpful if accident takes place when you're away from home.
Because anything beyond a quick check when you have the name needs time and a bit of work, it's often the other way around, in that it's the emergency (or a) contact that provides the ID - e.g. ringing your phone to find out where you are and someone else (Police/nurse) answers, or you don't come home and so they contact the police to flag you as a missing person, and then the description given is matched to the Jane Doe found unconscious in the woods.