Change of surname and parents name in birth certificate

Dear Sir/Madam,

Kindly advice me on the procedure to obtain a birth certificate with a changed sur name and changed parents name.

Facts:

1. My current birth certificate mentions a baby boy born to so and so parents (natural parents details)
2. I was adopted to my grand parents at the age of 4 and the adoption deed was registered
3. All my certificates and passport contains the family name of my grand father and my grand parents name in the father/mother section (as they legally adopted me via registering the adoption deed)

Hence, I would like to obtain a birth certificate with the following changes:

1.  With my full name as in the passport(including the family name of my adopted parents) and
2.  Parents details being changed to my adopted parents details instead of my natural parents

I already contacted the local muncipality to get the change done , showing my passport/certificates and the adoption deed as a proof but they mentioned, they cannot change the details or issue a birth certificate based on these.

Kindly advice on the procedure to have the above mentioned changes in my birth certificate.

Thanks in advance.

Best greetings,

Narayana Rao