The story
From the surname of a family that owned the house, whereas the surname was derived from reference to the Exchequer; more in Wikipedia at Chequers § Origin of the name.
Etymology from Wiktionary, CC BY-SA 4.0.
chequers
Today it means: A 16th-century manor house in Buckinghamshire, England, serving as the country house of the Prime Minister of the United Kingdom. Full definition →