Usually when one delivers a child at a hospital, DSS will come to the MOTHER and give her paperwork-birth/death certificate, SSN, paternity, etc. In the state I am in, both parents are required to go to a Vital Records office and both sign the birth certificate.
A friend of mine just had a child in California and she just went to the records office herself, put her and her husband’s name on the form. No questions asked.
If your wife is in the same disdainful state during delivery. She will be the one who decides the last name on the paperwork and at the records office.
If you are at the hospital and she does not want you there, surely she will call security to escort you out or before she delivers she can request that you are not to be allowed in the maternity ward. She can tell anything to the hospital security (like you are abusive) so you will not be permitted to see the delivery