I am a little unclear as to your situation. When the baby is born, you can refuse to put a name on the birth certificate. It would be up to the father to sign the voluntary proof of paternity (POP) declaration at the hospital. If he does not know about the child, or the birth, then he will not do that. There is no court proceeding unless you or the father initiate one by filing a Petition to Establish a Parental Relationship and asking that a paternity test be ordered. If your goal is to not have the father involved in the child's life, then you can probably get away with it. I would comment, however, that most children benefit from the involvement of both parents in their lives.
Please note that this answer does not constitute legal advice, and should not be relied on, as each situation is fact specific, and it is not possible to evaluate a legal problem without a comprehensive consultation and review of all the facts and court pleadings filed in the case. This answer does not create an attorney-client relationship.