Brannan is a surname. Notable people with the surname include:
John Brannan (1819–1892), United States Army officer who served in the Civil War and Mexican–American War
Mike Brannan (1955–2013), American golfer
Samuel Brannan (1819–1889), American businessman and journalist
Samuel S. Brannan (1835–1880), American politician and newspaper editor
Solomon Brannan (born 1942), American football player
Fictional characters:
Josh Brannan, character in the NBC series Last Resort