A grouping on SSN should do it
SELECT
ssn
FROM
Table t1
GROUP BY
ssn
HAVING COUNT(*) > 1
..or if you have many rows per ssn and only want to find duplicate names)
...
HAVING COUNT(DISTINCT name) > 1
Edit, oops, misunderstood
SELECT
ssn
FROM
Table t1
GROUP BY
ssn
HAVING MIN(name) <> MAX(name)
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