Leon Fulsone/Fulsom
I love when I can find out who the babies are! According to the back of the photo, this is “Leon Folsone” – and according to the front, he’s probably from Eau Claire, Wisconsin. I found little Leon for sale on Etsy if you’re interested in owning him (Link to Etsy store).
After some careful research I believe his name is actually Leon Folsom – or at least that’s what all the people who wrote his name on any document believed. There’s is no trace of a Leon Folsone (maybe it was just a misspelling). There is, however, a Leon Folsom born in Eau Claire, WI in 1893 and living there in 1905 with Mary and Fred Folsom. These are not his birth parents.
Leon was adopted, or so the 1910 Maple Grove, Idaho census record of the family states. The Folsom’s do appear to have one other child at least. The circumstances around his adoption aren’t known to me. Maybe some of his descendants know more, I’d love to hear the story.
Unclaimed Ancestors 
I looked more closely at the writing on the back of the photo and you can take the name both ways because of the handwriting. I bet you are correct in you findings with Folsom. Thanks for posting my photo.