The traditional definition of a counting house is a building or room used by the bookkeeping or accounting department of a business, according to Dictionary.com. The term comes from Late Middle English and may be hyphenated. The character of Scrooge from "A Christmas Carol" ran a counting house.
With a historical connection to finance, accountants and payment processing firms often choose to include "counting house" in their name. Some restaurants also use the counting house reference in their name due to a building's prior function: in London, The Counting House is a restaurant located in the converted Prescott's Bank, originally built in 1893.