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. In most cases, this is done with a certified copy of a birth certificate.
A certified copy is a copy from a state agency that shows that it is a correct copy of the original and can be used for legal purposes like applying for a passport or a name change. It may have a watermark, a raised seal, micro-printing, multi-colored background, printed with heat sensitive ink, or other security features to show that it is real.