they sure can. I got ginger and "carrot top" (couldn't figure that one out because carrot tops were green) but mostly I stung from "wet the bed" that rhymed with red-head and the proverbial fatty fatty two by four.
Another poor soul that came to mind was a chap whose last name was Eversfield who had unfortunate teeth and a penchant for breaking his leg ( twice in one year) who ended up with the nickname Gummie Evercripple.