If you name a mob then right-click the mob and it has a baby but the baby isn't named.
If you name a mob then right-click the mob and it has a baby but the baby isn't named.
Confirmed
babies, mob
Snapshot 13w04a, Snapshot 13w10a
Snapshot 13w10b
Retrieved
If you make a mob without a name and then create a baby with a named egg from the created mob the baby doesnt have a name => This is a bug yes