Since her marriage has been annulled, your wife has the option to use either her maiden name or her new married name without need of a court order.
If she is a first-time passport applicant, she only needs to present her birth certificate (BC) and the new marriage contract (MC). However, if she has an old passport with her old married name, she has to present the annulment decree in addition to BC and MC.
Here’s an excerpt from a Supreme Court ruling regarding use of surname/married name in the event of annulment of marriage
B. In the event of annulment of marriage —
(1) If the wife is adjudged to be the guilty party, she must resume her maiden name and surname, but
(2) If the wife is the innocent party —
(i) She may resume her maiden name and surname, or
(ii) She may choose o continue using her husband's surname unless —
a. The court decrees otherwise, or
b.
She or he remarries (Art. 371, Civil Code)And here’s the link to the ruling:
http://www.lawphil.net/judjuris/juri1995/f...94986_1995.html