An Anarch is a ruler of Yardistan.
The word 'Anarch' was created by Gryphon Avocatio to describe the ruler of an anarchy by analogy to the monarch of a monarchy. The title was intentionally nonsensical and self-contradictory, in keeping with Yardistani culture.
Having the title 'Anarch' is not synonymous with being Duke of Yardistan (or Count, for that matter). There is no requirement that Anarch and Duke be the same person, as the title Anarch exists outside of the Shirerothian legal system and is a purely Yardistani concept.