You should be able to correct your daughter's birth certificate using the evidence that the man named is not her father, especially if she is fairly young. Start by going to National Center for Health Statistics website to find your local Office or Department of Vital Statistics. Ask the representative there whether you can change your child's name on her birth certificate without having to go to court. There may be very simple forms you can download. If you're required to go to court to make the change, the Office or Department of Vital Statistics may be able to help you locate the right local county court.