John C. Foster, age 31 in 1940, living with his widowed mother Christian A. Foster in Newport News Virginia.

Question

Christian A. Foster was listed as head of household, a widow, who operated a boarding house in Newport News Virginia per 1940 census.  Son John C. was the only relative also living there.  Suspect his middle name was Churchill.

Answer 1

Looks like what you suspect is right. Wonder what the R. is short for in his father's middle initial, Julius R Foster.
John C Foster
Son
United States Census, 1940
birth:    1909    Virginia
residence:    1940    Ward 3, Newport News, Newport News City, Newport News City, Virginia, United States    
mother:    Christian A Foster
other:    Gilmor W Diggs, Madison C Bunch, William L Chaney, Russell H Setliff, Rum E Lathem        

John C Foster
Son
United States Census, 1930
birth:    1908    Virginia
residence:    1930    Newport News, Newport News (Independent City), Virginia, United States    
father:    Julius R Foster
mother:    Christian A Foster
other:    Lewis Taylor, Drucella Brizendine        

Churchill Foster
Son
United States Census, 1920
birth:    1908    Virginia
residence:    1920    Newport News Ward 3, Newport News (Independent City), Virginia, United States    
father:    Julius R Foster
mother:    Christine Ann Foster

Answer 2

Here is John C. Foster

Son United States Census, 1910 https://familysearch.org/ark:/61903/1:1:MPLW-JKC

Son United States Census, 1920 https://familysearch.org/ark:/61903/1:1:MJNP-7WM

Son United States Census, 1930 https://familysearch.org/ark:/61903/1:1:CHVC-1N2

Son United States Census, 1940 https://familysearch.org/ark:/61903/1:1:VR11-BFG

Find A Grave Index https://familysearch.org/ark:/61903/1:1:QVL7-362R