My son was 2 years old. I already get an birthcertificate with his current name. I need to change his name as per numerology. So, it is possible to change his name in birthcertificate also...

ANY question on law needs to include your general locale as laws vary by area.

A birth certificate is a legal document. Usually it requires a court order to change. It also requires the agreement of both parents.

Yes, where you live will decide the exact laws, but for the US, both parents will sign the forms for court and submit it along with the fees.