Synchrony Financial Credit Card Complaint

Synchrony Financial Credit card department,

Identity theft / Fraud / Embezzlement Minnesota

I received a credit card today from - ' Synchrony Bank that I did not apply for. When I contacted Synchrony Bank 's Fraud department, they refused to cancel the card unless I would give them my social security number. Since I do n't know the " bank '', I am not giving them any personal information other than the card number I want cancelled. They told me to research them & then call back when I would give them my SSN #. Possible identity Theft?