Father has no "right" to be in the delivery room nor does his family members. This is your call; just tell the hospital personnel when you are going to deliver as to who you do and do not want present.
When you are at the hospital the nurse will ask you to fill out the birth certificate information. You can name the child whatever you want, elect to list the father or leave the father's name blank. The problem is that it appears the father wuikll fight you on the child's last name. The only way for him to do this is to wait until the birth of the baby and then file a petition in court to have the child's name changed. I do not know your county's practices, but in Phladelphia, it is likely the judge will grant the name change petition if father testifies tht he is, or that he wants to be very active in the child's life. Therefore, you need to decide if its worth it. Maybe there can be a compromise - if the baby is a girl, hyphonate your two last names or if a boy, make your maiden name his middle name - just a suggestion .
You can not file for custody before the child is born, nor can father. Once the baby is born, either you or father, or both, can file for custody. I find it very unlikely that a judge will grant shared custody of a newborn to a father. He will get shared legal custody, but shared physical custody of a baby who is only a few weeks old, unlikely. However, as I said, I do not know your county or judges.