Often referred to as the "Fairbank" cocktail (no "s"), the earliest reports I find of this drink (July 22, 1907) clearly refer to it as "Fairbanks".

According to the Savoy Cocktail book, this drink was named after Douglas Fairbanks, but in 1920 (10 years earlier) Robert Vermeire in “Cocktails: How To Mix Them” probably provides the truer tale with indication that it was named after Charles Warren Fairbanks, who was Theodore Roosevelt’s vice president.