Doesn't matter if I have your social or not...
Name and current address, ANY piece of junk mail will have that, and I've got you...
All I do is run a credit check (Costs $35 from the major credit reporting companies) with just the name and street address, and they will give me your full & correct name, date of birth, social security number, drives license number, and in some cases, a list of your banks and credit cards, along with any mortgages and property you might own and if you are current or delinquent in your property taxes, yearly income and a break down of that income, earned or unearned, how may 1099's or W-4 forms you have on record, dependents, ect.
From there it's just a hop, skip & jump over to the state/county records (most are on line now) and punch in the tax numbers, and get back the tax records for the properties, vehicles (cars, boats, motor homes, trailers) and their registrations, criminal records, licenses for cars, trucks, boats, radio operations, hunting/fishing licenses, ect.
An increasing number of states are requiring special license holders to have their social security numbers on the license.
CDL (Commercial Drivers License) holders are increasingly required to have an ORIGINAL social security office issued card when loading or unloading at any government operations center...
Guys that carry stuff like military contractor parts, or if you have to enter areas like gated industrial parks or airports.
Many places are requiring an official copy of social security card and birth certificate, along with some places requiring things like voter registration cards...