Do I need to be online for it to deliver? If not, does it name itself automatically?
Does anything else happen such as growing up if I am not online?
Do I need to be online for it to deliver? If not, does it name itself automatically?
Does anything else happen such as growing up if I am not online?
You do have to be online to deliver a baby.
If a baby is about to be born when you're offline, i.e. three hours have passed, it will wait until you open the game again to come out :) You will be able to name him/her at this moment. A baby will never name him/herself automatically.
Considering that growing up essentially just adds the possibility to make a dweller work, what difference does it make if it happens offline?
To explain a bit more, nothing really happens "offline". The game does not continue to run when you do not play (even if push notifications on mobile can make you think so). This is what the game does:
You need to be online to deliver the baby.
It takes three hours for a pregnant woman to be ready to give birth. It doesn't matter if you're online or not, that's the minimum time it takes. Once the three hours have taken place, and you've logged back in if you've been away, you get an animation and a baby icon appears above the woman to show she's ready to give birth.
That's how she stays until you click the icon. She could remain pregnant forever if you don't deliver the baby. Once you do that, the child appears and you give it a name.
The child now needs another three hours to grow up. Again, you can be online or offline, it doesn't matter. But there's no icon clicking to do when going from child to adult - so if you deliver a child, then log out for more than three hours, then log back in again, you'll find the child has grown into an unassigned adult dweller.
So, to answer the three questions in your post in order: Yes, No and Yes.