The leotard is one of the few garments named after the person who made it famous, and he never called it that.
Jules Léotard was a French acrobat and aerialist. He died in 1870, according to Merriam-Webster and Etymonline. His birth year is less certain: Etymonline gives 1830 and Wikipedia gives 1838, and no source checked settles it. History Today says he developed his act at his father's house in Toulouse and dates his first flying trapeze performance to 12 November 1859 at the Cirque Napoléon in Paris.
His costume was a one-piece knitted garment, which Wikipedia says suited the safety and agility needs of trapeze work. Dictionary.com credits him with inventing it but notes that he called it a maillot. Wikipedia describes that as a general French word for tight-fitting shirts. It also says he designed the garment for men.
The English name came after his death. Merriam-Webster gives 1886 as the first known use, which Wikipedia describes as only 16 years after he died. Dictionary.com also says the garment was called a leotard in 1886. Etymonline records the plural leotards in 1881 instead, so the date varies by a few years depending on the reference.
Dictionary.com's headline date for the word is 1915 to 1920. That conflicts with the other dates, and the entry does not say which kind of evidence it refers to.
The garment changed owners over the decades. Wikipedia notes that circus performers wore it in the early 20th century. It says the disco craze and the aerobics boom of the late 1970s made it common exercise wear, helped by Jane Fonda's videos.
The word has also left its namesake behind. Etymonline says unitard, a one-piece garment, appeared in 1961 from uni-, "one," and an ending taken from leotard. A trapeze artist's surname is now a building block for new clothing words.