I'm Doug, and I'm very sorry to hear of your situation. My goal is to provide you with excellent service today.
The cop probably thought that you may be someone else, and that you were using a different name and ID----but without any proof of that other than a bare suspicion, he didn't have probable cause to further detain or arrest you.
Asking for your social---while inappropriate and possibly against department policy, would have allowed him to compare your information against the person he may have thought that you were.
It was inappropriate for him to lie about a requirement that you provide your social security number and because of the possibility of identity theft that exists, you probably should file a formal complaint against the office with his department.
You may reply back to me using the Reply link and I will be happy to continue to assist you until I am able to address your concerns, to your satisfaction.
Kindly, remember to rate my service to you. That is how I am credited for assisting you.
I wish you and yours the best this holiday season,