Source: https://legalaidatwork.org/factsheet/updating-your-social-security-number-with-your-employer/
Timestamp: 2019-04-26 00:03:22+00:00

Document:
I recently received a new Social Security number (“SSN”). Am I allowed to update it with my employer?
Yes. IRS Form W-4 states that you should “consider completing a new Form W-4 each year and when your personal or financial situation changes.” In fact, in California, employees have a protected right to update their personal information. See Cal. Lab. Code § 1024.6. Please be aware, however, that when you ask to update your SSN on your Form W-4 your employer may ask you also to complete a new Form I-9. At that time, you should simply complete a new Form I-9 with your updated SSN and original hire date. Your employer can then attach the new Form I-9 to the original I-9 you completed at the time of hire. See USCIS Employer Handbook at p. 24, available at http://www.uscis.gov/files/form/m-274.pdf.
When I attempted to update my SSN, my employer asked for more documents or different documents than the Form I-9 requires. Is this allowed?
No. In updating your SSN, your employer may not ask for more or different documents than required by federal law. Doing so may be discriminatory and constitute an unfair immigration-related employment practice. See 8 U.S.C. § 1324b; INA § 274B; 8 C.F.R. §274A.2(b)(1)(v); Cal. Lab. Code § 1019.
My employer has refused to allow me to update my SSN. What should I do?
If you live in California, you should inform your employer of your right to update your personal information. Please see below for a sample letter you can provide your employer, which explains that updating one’s personal information is protected under state law.
My employer fired me for updating my SSN. What can I do?
Under California Labor Code § 1024.6, your employer cannot fire, discriminate, retaliate, or take any adverse action against you if you update your personal information, unless the changes are directly related to the job’s skill set, qualifications, or knowledge required for the job.
If you feel that your employer has done any of the above, you can file a complaint with the Department of Labor Standards and Enforcement (DLSE). If the DLSE decides that your employer has committed such retaliation against you, your employer may face a penalty of up to $10,000 for each incident of retaliation or suspension of its business license for a period of time. For more information on how to file a complaint with DLSE, visit http://www.dir.ca.gov/dlse/HowToFileDiscriminationComplaint.htm. Your complaint must be filed within six (6) months after your employer’s retaliation against you.
Can I receive credit for the social security deductions taken from wages I earned before I received my own SSN?
Yes. This process is often referred to as “unscrambling.” The Social Security Administration (SSA) will allow you to update your records and receive credit for earnings you may have made while using a different SSN. The SSA can assist you in this process. For more information on what you need to update your records, visit http://www.ssa.gov/pubs/EN-05-10081.pdf.
Will I face criminal charges for updating my earnings records with the Social Security Administration?
Because using a SSN other than your own is illegal, there is no guarantee that you will not face legal consequences for having used a different SSN. However, the SSA does not typically prosecute (nor refer to prosecutors) people who have previously reported income under a SSN that was not their own.
Click here for a sample letter to use in writing to your employer.

References: § 1024
 § 1324
 § 274
 §274
 § 1019
 § 1024