How do you put the father's name on the birth certificate?

You could have signed the affidavit of paternity when the child was born (I'm assuming you're not married to the mother). Washington doesn't have custody as such. If what you mean is that the child lives with you the majority of time, it must be without a court order, which gives you no rights at all. Only a court order can make you the legal father of the child. If such and order was granted, placing the child with you, the order should have also given instructions to amend the birth certificate. If it didn't you can go back to court and ask the court to order that. If the child is living with you without any orders, you need to file a parentage action to make it all legal by getting the birth certificate amended, getting a parenting plan and a child support order. Without the parenting plan, the mother can take the child any time she wants, since in the eyes of the law you are not the father.

In Idaho you either file an affidavit signed by both parents stating that you are the father or you go to court and get an order to change the name.

Get a certified copy of the order declaring you the father . Get the change of birth certificate form from the county clerk. (or on line). Send it all to the Bureau of Vital Statistics with the correct amount of money. Wait six weeks.