Query on how to make a change &/or correction in my birth certificate

Am a Goan, born in Ahmedabad, Gujarat, in 1963 to parents who settled there, where I reside there ever since till date. My initial Primary School admission was based on the Church Baptism Cert, and so there was never a need of an official printed Ahmedabad Muni Corporation's Birth Cert. In fact all my official documents like the Aadhar, PAN, Ration, Elect & Tele Bills based on my SSC Leaving Cert do have my Name correctly spelt. But lately on getting the Muni BC noticed an incorrect First Name in my Own, my Father's & Mother's name too in the vernacular Gujarati language. My father & mother were both born in Goa during Portuguese times. My father expired in 1964 my infancy & have no official document except his Death Cert which too incorrectly merely mentions the First Alphabets of his First & Middle Name. My mother expired in Dec 2017 & do have her Aadhar, Ration Card, Death Cert too. After such a long lapse of time, pls do guide me if I can correct the First Names of my own Self & of my both Parent's as incorrectly mentioned in my BC, and elaborate as to how to go about it ? [ First Name change/correction: 1. Self : Incorrectly as JACOB i/s of correct TREVOR; 2. Father : Incorrectly as WILSON i/s of correct VINCENT; and 3. Incorrectly as CHRISTIANA i/s of correct CHRISPINE ]