Late Registration Complication

hi! my mother was already separated (not legally) with the man she married when she got pregnant with me by another man. that man (my biological father) took care of the registration of my birth wherein he is indicated as biological father and his surname, lim, became my original surname. my mother and my father separated years later. my mom filed for late registration of my birth for me to use, del rosario, the surname of the man she was married to (to save us from shame). from then on, i used del rosario on everything from school records, sss, tin, employment and passport. just recently, i was supposed to get a copy of my birth certificate from NSO, but they informed me that lim was filed first, therefore, the late registration for del rosario is invalid since the mother's maiden name on both applications was the same. since it appears that lim is legally my correct surname, how am i going to change the names on all important records of my life such as education, employment, insurance, SSS, TIN, etc?

Please help.