Are her parents now married? If not, does she have an affidavit of acknowledgement of paternity from her father? She cannot change her surname on her PSA birth certificate without either a PSA marriage certificate from her parents or an affidavit of paternity from her father.
As for the name discrepancy on her BC and other documents, she will either need to have her BC corrected or have some other legal name change document. BC correction would be the easiest. The US consulate will require a legal document explaining the name discrepancy/change. An affidavit from your wife will not be enough. Not sure how she even got a passport from DFA with a different name from what's in her BC, but hey, it's the PH government 🤷♀️
Also, NBI clearance will be required. Your wife must submit one at NVC stage, after the I-130 petition that you will submit for her has been approved. Her NBI clearance must include an AKA field listing all the other names she has ever used on legal documents.