The comedy team came together in 1969, when comedian Barry Took brought them to the BBC TV network and pitched them for a comedy sketch show. The BBC added the word "Circus" because the members were often referred to as a circus as they ran around the BBC complex developing the show.
The group added the word "Flying" to give it a World War I barnstorming air show persona. In fact, the initial name was to be Baron Von Took's Flying Circus, after the man who brought them together. It was changed to Monty Python's Flying Circus because the group felt the name Monty Python sounded more like a terrible theatrical agent, which Took, obviously, was not.