Simply you have to apply for the add name in Birth certificate in Sewa Kendra in your district. You have to submit an application form regarding adding names in the birth certificate along with supporting documents.
Application form cum Self-Declaration from Parent
Original Birth Certificate with one photocopy.
School certificate or passport or driving license or documents on which date of birth and name is mentioned.
Self-Attested copy or self-declaration for child less than 5 year
Applicant Residence proof – (Voter Card/Aadhar/ Passport/Driving License )