Mine is a nickname I was first given in school around age 13. Fresh into being teenage boys, it was very funny to go around referring to everything as 'hairy' (as in, "who stole my hairy pencil?"). With 'hen' being an abbreviation of part of my name, "Hairy Hen" was the inevitable result, and remained in use for quite a while. Among a few friends, I'm still called that occasionally even now.
It seemed natural, therefore, to adopt it as a screen name. I first used it on a Harry Potter website in early 2004. For whatever reason, I spelled it with all lowercase letters and an underscore between the words, and have usually used that same rendition ever since. I've had other screen names as well, most of them bizarre and some being oblique Tolkien references, but this is by far the one I've used most often.
(The irony of it was that at the time I was actually the least hairy of any of my friends by a considerable margin, though this may not necessarily be true anymore.)
Had I thought of it, I might have gone with "The Drink Inspector", which is what I called myself when I prank-called the Coca-Cola company one time, or a Monty Python kind of name such as Uxbridge F. Stool-Sample or Mrs. B. J. Smegma or something like that. lol