Bonham Street was originally called Tavern Street. It was renamed in 1858 in honour of Sir Samuel George Bonham, who was the Resident Councillor of Singapore in 1831-37, and then the Governor of the Straits Settlements from 1837-1843.
In the 19th century, the trading firm of Katz Brothers had their godown along Chulia Street with its back to Bonham Street. As a result, the local Hokkiens called the street Tuan Katz Thokorh Auboey, meaning "(street) behind Mr Katz's Warehouse".