The name Todd is not short for anything. It is a word in its own right. It means "Fox".
The surname, and later given name derives from the Middle English word for Fox (see below).
(see http://wiki.name.com/en/Todd#ORIGIN_AND_HISTORY)
The name Todd originates as a surname deriving from the Middle English "tod" or "todde" meaning "a fox." The surname probably derived to describe those who were fox hunters. In Scottish, the name "Tod" means "clever" or "wily."
Todd Joseph's birth name is Todd Rudisill.
Todd Brodie's birth name is Todd Brodzinski.
Todd Tesen's birth name is Todd Thiessen.
Todd Carty's birth name is Todd Jennings.
Todd Grinnell's birth name is Todd A. Grinnell.
Todd Hacker's birth name is Todd Michael.
Todd Nasca's birth name is Michael Todd Nasca.
Todd Kurth's birth name is Todd Lawrence Kurth.
Todd Louiso's birth name is Todd Scherer Louiso.
Todd Lasance's birth name is Todd James Lasance.
Todd Lyght's birth name is Todd William Lyght.
Todd MacCulloch's birth name is Todd Carlyle MacCulloch.