Is not meant here to be a person's actual name, rather, Woody Johnson, describes a hard penis, or a man who has one.
Foxy Chick: Damn! John Doe started taking Viagra last month. Yesterday he was "Woody Johnson" for about 3 and a half hours. We both came at least 6 times!
by Annie Johnson June 01, 2006
A very hard and erect penis.
I got a woody johnson just looking at that elevator chick over there!
by Jack Bozdog June 07, 2006