[Facts] Re: Dash/Hungarian
Sorry I can't help you with the nickname, as it could be a totally new name which your great-grandfather picked up or which was given to him by friends when he became "Americanized".
Have you tried searching the U.S. Federal Census records? If your grandfather went by his actual name in the first few years after immigrating to America, you may find out what that name was in those records.
-- Nanaea