On the 1850 Census, his name appears to be "Willson" age 7. There is no second dotted "i" in his name to indicate "William". And he is the son of Allen & Gilly on that census. Gilly died durin child birth in 1851, and Allen shortly after in 1852 when Wilson was 9. Wilson was listed as one of three minor children upon Allen's death: http://interactive.ancestry.com/9048/007820614_00878?pid=254...
By 1860 census, he's living with his sister, Drusilla Faw, and their mother Gilly's parents, David & Mary Fouts. His name is William in 1860. He is listed as 16.
Hope this helps!