The fedora is named after a woman who never existed. Fédora is the heroine of an 1882 play by the French dramatist Victorien Sardou, and the hat took her name.

Sardou wrote Fédora for Sarah Bernhardt, who played the title role, a Russian princess named Fédora Romazoff. The play was a hit, and its name was soon attached to fashionable goods. According to the Oxford English Dictionary, the play's title and heroine seem to have been borrowed first for various items of women's clothing, including hats.

The familiar story says Bernhardt wore a soft, center-creased hat in the role and that women copied it. Wikipedia repeats this, adding that the hat later became a symbol of the women's rights movement. The OED is more careful. It says the precise connection between the play and the hat is unclear. Word Histories adds that the hat Bernhardt wears in a photograph of the play looks little like the later fedora.

Here is the odd part. The OED notes that the soft felt fedora was first marketed as a men's hat. It finds no contemporary evidence linking the style to anything the play's male cast wore. Word Histories suggests the name was picked for its air of French elegance. In 1883 Fédora was being attached to many fashion items, from bonnets to men's hats.

The dates suggest a quick borrowing. The OED's first English citations are from 1883 and 1884, a year or two after the Paris premiere. Word Histories finds a Knox the Hatter advertisement for "The 'FEDORA'!" in the New York Sun of 26 September 1883. Wikipedia gives a later picture, saying the play reached the United States in 1889 and the term was in use by 1891.

The hat's biggest years came decades later. Wikipedia credits Edward, Prince of Wales, with making the hat popular among men after he began wearing it in 1924. Its height of popularity ran from the 1920s to the early 1950s. It faded in the later 1950s as clothing became more casual.

It has plenty of company. Several hats are named after whatever was fashionable when they appeared, from a novel to a spa town to the man who made them.