In England it’s properly called a “darby,” but everywhere else, including here, it’s known as a “derby.”
In 1780, the twelfth Earl of Derby was having dinner with his friend Sir Charles Bunbury when they decided to sponsor a horse race for three-year-olds in Surrey, England.
They tossed a coin to decide after which of them the race would be named and Derby won, otherwise the most exciting two minutes in sports would be the Kentucky Bunbury.
That’s why is a horse race is sometimes called a “derby”.