I'm Lucy, and I'd be happy to answer your questions today.
To add you name to a child's birth certificate as a parent, the first step is to file a Petition to Establish Paternity, which puts the mother and the court on notice that you're attempting to create a legal relationship here. (Either parent can actually file this.) You can ask the judge to order the mother to present the child for a DNA test. When it comes back, the judge will issue a court order that you are the parent, which can be used to add your name to the birth certificate. At the same time, the judge will enter orders for child custody and child support. The court actually has forms for establishing paternity available online:
If the parents can agree on a parenting plan, the judge will usually sign off on it. If you can't, then the judge will look at a variety of factors to determine what is best for the child. The judge starts with the presumption that a child benefits from having a relationship with two biological parents rather than one.
Changing a baby's last name requires a Petition for Name Change of a Minor Child. Paternity must be established before the judge will entertain the motion, but it is possible to file both at the same time. He'll just put the name change on hold until the paternity test comes back. If the other parent won't agree to the change, both parents will have an opportunity to explain to the court why the name they prefer would be best for the child. Here is a form for that:
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