The Last Order
Thankfully nothing to do with occult mysteries, secret societies, conspiracy theory or the generally arcane.
The name evokes the time-honoured cry of the British publican at closing time: "Last orders, please!", which, as anyone familiar with British pubs will know, provokes a rush to the bar for several drinks each, closely followed by a desperate period of binge-drinking, trying to get it all down your neck in the half-hour or so while "Time, gentlemen, please!" inevitably becomes "Have you got no homes to go to?".
In the manner of these things, people who have been drinking together as undergraduates for over three years will see no reason to cease just because they have passed their final exams and become fully-fledged wizards.
As the group of socially-drinking wizards grew in power and experience, the thought many well have occurred, round about the tenth pint of Winkles Old Peculiar or Turbot's Really Odd, "Hey, why don't we form an Order of Wizards? That'll REALLY show those stuck-up miserable buggers in the Order of the Silver Star!" etc, etc.