If you so choose. It is not necessary. I think its better that you do that once you receive your green card, so that the SSA can issue you a new card with no restrictive notes on it.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
If you are an F-1 or M-1 student, and you showed your Form I-20, Certificate of Eligibility for Nonimmigrant Student Status and other required documents to the SSA. to get a legal SSN and still have the same name, you do not need to do anything else. If you are changing your name based on marriage, keeping all legal documents with the EXACT same name is the best practice.
This is not necessary unless your social security card has any restrictions on it.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.