Says imdb:

The many variations of just how Gibson earned the nametag "Hoot:" (1) As a youth, he loved to hunt owls; (2) while a teenager working on a rodeo ranch, other ranchhands called him "Hoot Owl" and that the name was shortened to just "Hoot"; (3) he earned the name while a messenger with the Owl Drug Company; and (4) while touring briefly in vaudeville, he would hoot when the audience cheered and, thus, the nickname.

Not one sounds plausible.