The 'Keeping Up With The Kardashians' star revealed the unusual choice as well as the baby's weight, a healthy eight pounds, one ounce.
Alongside a picture of four emojis resembling her growing family, she simply wrote: "SAINT WEST (sic)"
We couldn't helf but wondering if their honeymoon choice of the Catholic island of Ireland had helped them in their choice? Is that St. Patricia or St. Jude?
The 35-year-old television personality - who already has daughter North, two - gave birth to her second child on Saturday, nearly three weeks ahead of her due date of Christmas Day.
It has not been an easy pregnancy for Kim, who recently revealed she had to undergo an External Cephalic Version procedure to have her baby moved from the breech position.
She wrote: "This weekend I checked into the hospital and underwent a procedure called an ECV (External Cephalic Version, or a Version), which is done to manually turn the baby from a breech position to a head-down position
"They gave me an IV with medication to relax my uterus, and then three doctors attempted to work together to turn the baby. There was a risk that my water might break or the baby's heart rate could drop - in which case, an emergency C-section would then take place. I went in with my sisters and my husband. I was prepared for it all! (sic)"