Be careful when you fill out your baby's full name and your mailing address. Correcting a birth certificate can cost money or even require a trip to court.Birth Certificates can be ordered online. Overview: Vital Records has birth records (since 1881) for all of New York State except New York City. You cannot request a correction online. You must be able to prove where you or the child was born if you want to change your name or your child's name. You don't have to submit them in original. The required Affidavit of Amendment to Certificate of Live. L.I.C., Queens, 11101. That person must then fill out an affidavit of mail service for you to give to the court.