I went and came back from mexico with AP and have the same thing passport maiden name and AP married name and not once was I questioned. I did take my marriage certificate just in case.
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Application received 9/14/12 Ca Service Center
Biometrics 9/24/12, e-request 3/14/13
Approved 4/30/13, Letters received (765&821) 5/2/13
Ead 5/4/13 ss 5/8 CA id&written test 5/8 DL passed 5/13