What is the name Todd short for?

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."