Bransby is both a given name and a surname. Notable people with the name include:
Given name: Bransby Cooper (1844–1914), Australian cricketer Bransby Key (1838–1901), South African Anglican bishop Bransby Williams (1870–1961), British actor, comedian and monologist Eric Bransby Williams (1900–1994), British actor
Surname: Bruce Bransby, American double-bassist Eric Bransby (1916–2020), American artist James Hews Bransby (1783–1847), English Unitarian minister Lawrence Bransby (born 1951), South African writer