A, Lullaby Jane. It has a nice personal touch to it.
Lullaby Jane is much better than the second option. Style Icing says nothing about babies, and the ice in Icing sounds cold, brittle - not warm and fuzzy. You want a name that consumers can resonate to, and will in some way associate with babies, and a lullaby falls into that category, although it makes me think more of sleepwear and cradles than diapers. Maybe look for a third option.
Definitely LullabyJane! It gives an indication of what type of merchandise you are selling since lullabyes are usually linked to babies. Good luck with your business, it sounds like a great idea!
I think LullabyJane would be best because if you name it Style Icing people might think it has cosmetics and assesories in it. Also LullabyJane is really cute!
