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 Tesen's birth name is Todd Thiessen.
Todd Joseph's birth name is Todd Rudisill.
Todd Hacker's birth name is Todd Michael.
Todd Grinnell's birth name is Todd A. Grinnell.
Todd Carty's birth name is Todd Jennings.
Todd Brodie's birth name is Todd Brodzinski.
Todd Sauerbrun's birth name is Todd Scott Sauerbrun.
Todd Sachs's birth name is Todd Alan Sachs.
Todd Sand's birth name is Sand, Todd Kenneth.
Todd Rotondi's birth name is Todd Michael Rotondi.
Todd Pratt's birth name is Todd Alan Pratt.
Todd Pesko's birth name is Todd Joseph Pesko.