This has been driving me nuts for a while. We have the following adjectives to describe a particular period in history, mostly British history:
Elizabeth = Elizabethan
James = Jacobian
Charles = Carloinian
Henry = Henrician
Mary = Marian
George = Georgan
Victoria


What would be the appropriate adjective to describe the reign of Queen Anne or the future King William?

In literature, there's the Augustan that covers Queen Anne, George I, and George II. There's also Tudor, Restoration, Stuart, Hanoverian, Regency, and Edwardian.

Hello,
Tudor would cover Elizabethan, Marian, Edwardian and Henrican.
Stuart would cover Jacobian, Carolinian, and the new Marians.
Hanovarian would Cover Georgan and some might say Victorian and the New Elizabethans. I still wonder what the adjectives would be Specifically for the periods with a Queen named Anne or a King named William.

I misunderstood. I thought you wanted the term for the period Queen Anne, the last of the Stuarts, was reigning. I don't think you'll find a latinate adjectival form for Anne or William. But here goes.

The term in English for Wilhelm II of Prussia is wilhelmine. The Latin for William is Gulielmus, so you could coin an adjectival form like the others, gulielmian, or maybe gulielmite. For Anne, how about Hannan, Hannian, or Hannine? They're all made up, but might be understandable.

in furnature, Queen Anne is a style name that exist on its own.
(that is queen Anne that was the Stuart!)

It is British to use the king or queen's name as an adjective for a period or style only ? Do they never say : period Henry V or period Anne I or Elisabeth II? . (Queen Anne style is remarkable as maybe an exception, which is interesting)). We talk about Victorian furniture, paintings, sculptures. Edwardian style.
Continental periods are period + name: period Louis XIV , but also adjective before period : Habsburgian and Napoleontic period . So after the Beatrix period or period Beatrix we will have the Willem Alexander period or period W. A.