Can the mother see and hold the baby after the birth?

Yes, the new mother can do anything any other mother may choose to do. She has not relinquished any of her parental rights at this time. She has the right to see, hold and care for the baby, and name the baby. However, if she doesn’t want to do any of these things, she has the right not to and still be treated with respect by hospital staff. In adoption, this is referred to as the birthing plan. She is the parent who signs the birth certificate and may choose any name for the baby, including the name the adopting parents selected, if that is her choice.
If she has chosen a family to adopt the baby, she may request THEY be the ones to care for the baby in the hospital. She may also request they be in the delivery room.