We do not currently know of any antonyms for social security number.
The noun social security number is defined as:
A nine-digit number issued to citizens, permanent residents, and temporary (working) residents under section 205(c)(2) of the Social Security Act, codified as 42 U.S.C. ยง 405(c)(2). The number is issued to an individual by the Social Security Administration, an agency of the U.S. Federal Government. Its primary purpose is to track individuals for taxation purposes. Abbreviated as SSN. In recent years the SSN has become a de facto national identification number.