The chubby baby that has the "Hungry Man" as his Father is "Nathaniel" I thought he was adorable and I also really liked "Rita" the little girl with the red hair and ponytails.
 
If anyone is interested, I wrote down some of the names and descriptions of the babies as I was playing, but unfortunately I didnt get the last 3 or 4 names. Maybe someone could add them or I will when I replay the game next. :)
 
William - "Well rounded baby"
Doris - "loves naps"
Aikiko- "No telling what she will want next"
Nathaniel - "Boy does he get hungry"
Rita "Makes lots of diaper messes"
Claude- "Loves playing with toys"
Felicia "Loves to play AND eat"
Maria
Annabelle " Loves to play"
 
 
Plus a few others  TBA  :)

I actually love the baby that's on the main screen. I was a little confused with the beginning of the story. Who is that chick in the picture and at the diner later on. His sister? So would that make that baby his nephew? Either way, I think he's adorable.

My second favorite baby is, um, I think Felicia. Is she the African-American girl? Because that's who I mean. She's relatively patient and adorable.