Take the court documents showing the name change to the Social Security Office. In addition, you will need documents showing your identity and US citizenship. Passport, ID, Drivers license, Birth certificate are all acceptable. You will fill out a new application for Social Security Card due to name change. Once your application is processed, you can proceed to DMV and change it there. You will probably will have to wait for 7-10 days for the changes of SSN record to go into effect.
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You'll need to take documentation of the new name with proof of identity to a Social Security office ad complete their paperwork. Once that is complete (wait about 10 days or so), then take all of the documentation to the DMV.
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