Please wait at least ten days after your ceremony before going to the Social Security Administration (SSA) to ensure that data reflecting your naturalization has been updated. You will need your Certificate of Naturalization or U.S. passport when you visit the SSA to update your record.lease wait at least ten days after your ceremony before going to the Social Security Administration (SSA) to ensure that data reflecting your naturalization has been updated. You will need your Certificate of Naturalization or U.S. passport when you visit the SSA to update your record.