Confusion regarding my identity.

I'm a son to my parents that were never married along with my two siblings. Our father left us when we were still young and we only had our mother to take care of us. Growing up, I've been using my mother's surname but when college came, I found out that it was not my real surname, that the surname registered in my birth certificate was my father's surname, not my mother's. The confusing thing is that my two siblings are with the same surname as my mother is and I'm the only one who's named after my father. I have not seen or been in contact with my father for a decade since he left us when I was young up to present date. How can I change my surname so it can be the same with my mother and two siblings? Hoping for your reply. Thank you.

petition for correction of birth certificate to be filed in court will be the proper remedy