Relatively easy if you have the Affidavit to Use the Surname of the Father (AUSF).
This is filed by your father or mother or guardian but not by you as you are a minor at Local Civil Registry Office (LCRO) where you were born.
Filed with the AUSF are Certificate of Live Birth with accomplished Affidavit of Acknowledgement/ Admission of Paternity at the back.
Rules are different for those registered with a Certificate of Live Birth and for those with no record yet with the Civil Registry Office. Likewise there are rules for minors and children of age.
For references, read the Republic Act 9255 at the psa.gov.ph site.
For details on fees, timing, inquire at the Civil Registry Office. Filing is one activity, registering with the NSO is another.