Source 1:

The word Derby probably originated from the football match held in Ashbourne, Dyers, Derbyshire, central England, on Confession Tuesday and the first day of Lent. It started in 12 century and was held from 2 pm to 10. The whole town was divided into two teams. The players were born in Hempel Creek, which flows through the town. One team is called "Upper Ades" and the other team is called "Lower Ades". Longmen is three miles apart, and games are played in the town. This is a famous local festival.

Source 2:

Another theory originated from the Derby Horse Racing founded by 1780 Earl of Derby 12. "Derby" is a small town in England. Derby is the place where horse racing is held in England. The horse racing produced by Derby is even more famous in the British horse racing industry. After 1870, sir. Derby founded the British Jockey Club. He holds a horse race in Epsom near London on the first Wednesday of June every year. This is one of the most famous horse races in Britain, and this day is also named Derby Day. In horse racing, most horses come from Derbyshire, and "Derby War" is used to describe "the race between horses from Derbyshire". Gradually, "Derby" was extended to other sports fields, and the British quoted it to describe the fierce competition between two teams in the same city. This is a derby.