At midnight the next day after your tama had the baby your tama who had the tama will leave and then the screen will saay boy if its a boy or girl if its a girl and will have that thing up to name it. Baby tamas are very needy so make sure you keep an eye on him or her and pause it when you cant.
They get sick a LOT. and when the parent dies, the baby will sleep the rest of the night. I wouldnt suggest trying to wake it up. I did that and it almost died. and its not always 24 hours. its AT LEAST 24 hours. Mine e lived for 4 days after he had his baby.