Actually the ones with a bill, like a baseball cap, that they wear on most construction sites, are called Bump Caps. Most injuries are from bumping your head on shit, rather than falling objects.
Your style, with the 360 degree brim, are I believe called Lineman's. Good for outdoors, to ward off the Sun, rain, and shit dropped by the guy up the pole you're working next to... and the guy going to kick the shit out of after work.
