Doesn’t mean anything really. The group had a whole list of ideas for the show’s name; one of which was “Gwen Dibley’s Flying Circus”. This was dropped because Gwen Dibley was an actual name. One of the group (Terry Jones I think) liked the name “Monty” because he felt it sounded seedy. “Python” was added on at random because they liked the sound. These ideas were then combined into the final name.
Another possible name was Baron von Tooks’ Flying Circus, as Barry Took had something to do with the formation of the comedy group, dont know the details though.
The story they told in Aspen was that the show’s preliminary name was Bunn, Wackett, Buzzard, Stubble and Boot, whereas the name BBC used in their schedules was Barry Took’s Flying Circus (Barry Took was the BBC bigwig responsible for the show). BBC wouldn’t let them use Bunn, Wackett, Buzzard, Stubble and Boot, so they had a brainstorming session trying to come up with a name.
They liked the “Flying Circus” part, and Michael Palin had just spent a weekend at his mother-in-law’s, where he saw the name Gwen Dibley in a magazine. He thought it would be a great idea to give someone a TV show without them knowing it, and so wanted to name the show Gwen Dibley’s Flying Circus. I don’t recall why they didn’t go with that name.
Anyway, one of them said that they should have a name that was slimy and slithery, and they all shouted “Python!”. Then someone yelled out “Monty”, which got laughs because Monty is Lord Montgomery, the war hero. And there it was: Monty Python’s Flying Circus.
I don’t know when Monty Python made the transition from being part of the title of the show to being the name of the group, though. It wasn’t intended that way to start with.
Another succinct summary was once provided in an interview with Terry Jones. They called the show that because “There was nobody called Monty in it, there was no python in it, it had nothing to do with flying and it wasn’t a circus”.
They typically played around with the credits of the show quite a bit of course, but the six episodes from the last season (1974), in which John Cleese does not appear, do mostly seem to refer to themselves as “Monty Python” and not “Monty Python’s Flying Circus”. Cleese is given what amounts to a writing credit in two of these episodes.
Didn’t Hazel Pethig feature in one of the early title ideas as well. It seems I heard that name come up in an interview with the cast probably in the making of the Life of Brian.
Hazel Pethig was the costume designer for Monty Python’s Flying Circus. It’s a spellbinding name, though, and it may well have figured in their early musings.