The marriage certificate is all she needs to update her name with SSA, she could've done that years ago, or 6 months ago, or whenever she wanted to after your wedding.
The name change document that she got when she naturalized (form N-662) is signed by a federal judge, you can cross "court order" in the application. USCIS cannot change someone's name, it has to go through court, hence it's a court order. Form N-662 is the the name change document.