How did Monty Python get its name?

Apparently a "Flying Circus" was a term used by troupes of performers, so there was some precedent for the name.

The term 'flying circus' was also another name for the popular entertainment of the 1920s known as barnstorming, where multiple performers collaborated with their stunts to perform a combined set of acts.

It appears the name came from prolonged brainstorming for names by the members. They kept changing the name, and one day BBC told them the most recent name (Flying Circus) had been printed in schedules and could no longer be changed.

Several names for the show were considered before Monty Python's Flying Circus was settled upon. Some were Owl Stretching Time, The Toad Elevating Moment, A Horse, a Spoon and a Bucket, Vaseline Review, and Bun, Wackett, Buzzard, Stubble and Boot.

Flying Circus stuck when the BBC explained it had printed that name in its schedules and was not prepared to amend it.

Other variations on "Monty Python's Flying Circus" were considered:

Many variations on the name in front of this title then came and went (popular legend holds that the BBC considered Monty Python's Flying Circus to be a ridiculous name, at which point the group threatened to change their name every week until the BBC relented).

Gwen Dibley's Flying Circus was named after a woman Palin had read about in the newspaper, thinking it would be amusing if she were to discover she had her own TV show.

Baron Von Took's Flying Circus was considered as an affectionate tribute to Barry Took, the man who had brought them together.

Arthur Megapode's Flying Circus was suggested, then discarded. The name Baron Von Took's Flying Circus had the form of Baron Manfred von Richthofen's Flying Circus of WWI fame, and the new group was forming in a time when the Royal Guardsmen's 1966 song "Snoopy vs. the Red Baron" had peaked.

https://en.wikipedia.org/wiki/Monty_Python#Monty_Python.27s_Flying_Circus