Having done ATC time at GA airports in SoCal, the only time I've ever heard a 172 or PA28 called "company" on freq was when it was from the same flight school. I would point out, however, that my lack of exposure to
other uses of the term as applied to light aircraft does not prove that the term is only used in the way I've heard it used. In other words, I've not been all places at all times, much as I've tried.
Dave