Corrected Card for a Noncitizen Adult 
If you change your name, become a U.S. citizen , or your immigration status or work authorization has changed , you need to tell Social Security so we can update our records and when necessary, issue a new card. When you request a replacement or a corrected Social Security card , you must show us proof of your identity, immigration status and work authorization. In addition , if you need to change or correct any information on your Social Security card , you need to show us certain documents about the change. We can only accept certain documents. 

What documents do I need to prove my identity? 
Social Security will ask to see your current U.S. immigration documents. Acceptable documents include : I-551 Permanent Resident Card I-94 Arrival / Departure Record with unexpired foreign passport, or admission stamp in the unexpired foreign passport ; or I-766 Employment Authorization Document , EAD, work permit from DHS. Important You must present original documents or copies certified by the agency that issued them. We cannot accept photocopies or notarized copies. All documents must be current not expired. We cannot accept a receipt showing you applied for the document. We may use one document for two purposes. For example , we may use your U.S. passport as proof of both citizenship and identity. 

What other documents do I need? 
Name Change If you legally change your name because of marriage, divorce, court order, or any other reason , you should tell Social Security. If you are working , you also need to tell your employer. If you do not tell us when your name changes , it may : Prevent your wages from being posted correctly to your Social Security record, which may lower the amount of your future Social Security benefits. Cause delays when you file your taxes. You must show us proof of your legal name change. Documents Social Security may accept to prove a legal name change include : Marriage document ; Divorce decree ; Court

user: Hello I need to change some information on my Social Security card.

assistant: Have you recently changed your name, or become a U.S. citizen?

user: I am now considered a U.S. citizen.

assistant: Due to the change in your immigration status, Social Security must be notified so we can update our records.

user: What documents do I need to show?

assistant: To show proof of your new status we only accept the following documents:
U.S. passport ;
Certificate of Naturalization N-550/N-570 ;
Certificate of Citizenship N-560/N-561 ;
Certificate of Report of Birth DS-1350 ;
Consular Report of Birth Abroad FS-240 , CRBA

user: Are there any other documents that I need to show?

assistant: You are also required to show us your I-20 Certificate of Eligibility for Nonimmigrant Student Status.

user: Do I need to prove that I'm still a student?

assistant: If you are an F-1 student we need a status letter from your school identifying you as such.

user: Do I still need to keep my immigration documents?

assistant: Yes in order to prove your immigration status you must show us your current U.S. immigration document consisting of either:
Form I-551 Lawful Permanent Resident Card
Machine Readable Immigrant Visa
I-766 Employment Authorization Document , EAD , work permit