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To change your name on your Social Security card: 1  Complete an Application For A Social Security Card (Form SS-5); and. 2  Show documents proving: 3  Legal name change; and.4  Identity; and. 5  U.S. citizenship (if you have not already established your citizenship with us), or immigration status if you are not a U.S. citizen.o change your name on your Social Security card: 1  Complete an Application For A Social Security Card (Form SS-5); and. 2  Show documents proving: 3  Legal name change; and.
The name attached to your Social Security number can change, however, if you go follow the right procedures. Jane Smith can take on her new husband's last name and become Jane Brown; or, as a nod to the name she was born with, she can use a hyphenated last name on her Social Security card: Jane Smith-Brown.he name attached to your Social Security number can change, however, if you go follow the right procedures. Jane Smith can take on her new husband's last name and become Jane Brown; or, as a nod to the name she was born with, she can use a hyphenated last name on her Social Security card: Jane Smith-Brown.