Change of name or date of birth cannot be made in the birth certificate.
If you have proper documentary evidence to prove that your date of birth is error in your birth certificate to that of the actual date of birth as per the substantial documentary evidences in your possession, you may file a suit for declaration before a civil court and get a court judgment for rectifying the error by a direction of court top the concerned authorities.
The name cannot be changed through court case, you can follow the name change procedure as per law.