If the father is not on the birth certificate, can my boyfriend put his name on it as the father or does he have to adopt my child when it's born?
Although I understand that you want to give your child a father, this is not the way to do it. It is illegal. In addition, it is very important that your child know who their biological father is even if they are not presently in their life. The reason for this is that they may need to find them for medical information. At this point that is usually only necessary in very unusual situations, but it is clear that medical treatment for the next generation will be tied to genetic information so it is very important that everyone have accurate information about their biological parents.
Your boyfriend can adopt your child, but first you will need to terminate the rights of the biological father. To do this you will need to consult a family law attorney especially if he is unwilling to voluntarily terminate his parental rights.
Once you are able to get his rights terminated, the adoption can be done by an adoption agency or adoption attorney in your state. It will require a home study to determine that your boyfriend will provide a safe physical and emotional space for your child. In addition, there is a criminal background check.