I think it has two meanings.
One: a name derived from a signature fighting technique he uses.
In this picture, Tawara is shown getting ready to blow away a charging sedan with a 'double-punch' move.
Put in a dire situation, a person will usually react with an action that she/he is most used to.
Tawara may have reacted by pulling out his "signature move"...a full powered double fisted punch, which perhaps has earned him the nickname.
Two: a pun later added to that name.
Since he flunked two years of highschool, that could be called a "Double Impact"...
So, here's my theory.
Any others?
