Soi Cowboy is named after T. G. "Cowboy" Edwards, a retired American airman who opened one of the first bars there in 1977.
A tall African-American, Edwards got his nickname because he invariably wore a cowboy hat, and he ran the Cowboy Bar on that Soi.
photo of TG Cowboy Edwards supplied by Bangkok Eyes.
additional information on the history can be found here:
Soi Cowboy history.