The drs in the hospital will care for your baby. You can ask them lots of questions too as you get ready to take your little one home. You’ll need to take your baby to their first Dr appt about 2 days after discharge, so that is your deadline. Ask your OB if they have any peds they recommend. Then use yelp reviews and do a quick interview if you have the time/opportunity.
Nothing happens if you do not choose one. There is always a pediatrician on call in the hospital for births. And the hospital can assign once the baby is born.