Mom's with Medicaid is the baby covered under you?

๐ŸŽ€S
When the baby is born do they automatically have Medicaid under you? They already sent me and "unborn" card for them, does that mean they're covered? And do I call to change his name and stuff? Or is he under my insurance? 
*UPDATE* 
Okay I know what to do now ๐Ÿ˜Šthanks so much for answering ladies ๐Ÿ’•๐Ÿ’š๐Ÿ’œ