In an article from The Fort Wayne Daily Gazzette from July 26, 1881 they referred to him as the noted desperado of Fort Sumner. Another member, CYAN, earlier had listed a link to some old newspaper articles about Billy the Kid and this is where I saw it. In another thread I had questioned this nickname as well, and even asked if it was possible that Ash Upson had wrote this particlular article. It had some other wording and stories that sounded very similar to Garrett's book which was ghost written by Ash Upson. Below is the first paragraph of the article:

LAS.VEGAS., N. M.. July 18. The
Daily Optic to-night give an interesting
account of the killing of William
Bonney, alias Billy the Kid, the
noted desperado, at Fort Sumner on
Thursday night.

The link to this website is:

http://www.cynthia splace.net/billy_the_kid.htm

I think it is an interesting question.