The bowler hat, also known as a Coke hat, is a creation of Victorian England. It has been said that the name arises from 'bowl' due to the hat's rounded shape; it has also been plausibly ascribed to the club players of the sport of bowling. One most compelling version, however, manages to explain both common use names for the hat.

According to The Man In the Bowler Hat: His History and Iconography, the first such hat was ordered by William Coke II. It was designed for him in 1850 by two hatters in the London fashion district of St. James Street named George and James Lock. They, however, did not manufacture the hat but rather conveyed the design to a supplier south of the River Thames - the factory of Thomas and William Bowler, who produced the original example and then began regular production. According to this source, the hat was known as a 'Bowler' south of the Thames in the working-class areas familiar with the Bowler factory, and a 'Coke hat' in St. James Street by the original purveyors the Locks, after the name of the client who commissioned it.

The bowler and the derby hat, it seems, are the same item; the derby was an American name for the hat after the Earl of Derby wore one to the Epsom Derby thoroughbred races and set a fashion. The hat itself is rounded, a slightly raised dome over a medium-width brim that typically curls upwards significantly on the sides. They are black in color, and may be banded. During their production they are given a coat of shellac or other varnish to make them stiff; unlike soft dress hats, the bowler/derby does not conform to the wearer's head shape. Some famous bowler wearing characters include Laurel and Hardy (who are mostly credited with wearing 'derbys') Major John Steed of The Avengers and the Thompson Twins of Tintin fame.

Fred Miller Robinson, The Man In the Bowler Hat: His History and Iconography. University of North Carolina Press; Chapel Hill, 1993.
The 'derby vs. bowler' correction is based on the commentary on several online hatters' sites, such as http://www.hatsinthebelfry.com/page/H/CTGY/derby_bowler_hats, http://dadshats.com and http://www.millerhats.com/hatcare_index/derbycare.html.