ako_si_momo

Thank you very much, hope you have a great evening

From the PH Consulate in Houston website:
 
Report of Marriage: https://houstonpcg.dfa.gov.ph/index.php/consular-services/civil-registry/report-of-marriage
Passport renewal: https://houstonpcg.dfa.gov.ph/index.php/consular-services/passport-services

@RO_AH is correct: you will need to do the Report of Marriage with the PH consulate that covers your state. With this document, your wife will be able to apply for a Philippine passport in her married name.  You don't need to go through a court for her legal name change.
 
Without the Report of Marriage, the consulate may still renew your wife's passport, but only in her maiden name.
 
If your state is covered by the PH embassy in Washington DC, here are the requirements: https://philippineembassy-usa.org/e-passport-renewal/
 
If your state is NOT covered by the DC embassy, search for the exact requirements on the consulate website.

Others will correct me if I am wrong. Your marriage is the legal process in which her name was legally changed so nothing to worry about there. I am not sure if she will need to do a ROM (Report of Marriage) before getting the passport in her married name, I think she does. I don't think that they will just accept your marriage certificate.