There are a couple of legal options on how the woman can her new name after getting married.
First, the most common one; The woman carries her husbands surname/familyname.
If Maria Gonzales marries John Cruz, She becomes Maria Cruz.
Second, this options is common in prominent family marriages; The woman appends her husbands surname.
If Maria Gonzales becoms Maria Gonzales-Cruz.
Third, this is also a common option for famous individuals such as celebrities or public officials. The woman retains her maiden name; she becoms Maria Gonzales.
Once you’ve decided on your “married name”, You know have to update your public documents to your new name and change your civil status to “M”-married. Not all public documents needs to be updated though, here are some of the documents that will need updating but not limited to: SSS, TIN, BIR, Insurance, Bank Accounts, etc…