In-universe, all the various names were probably applied and correct at one point or another, but there's not a clear/official timeline for which applied when.
Note that the nearby Trinity Worlds were variously known as the Southwestern Worlds, Intendancy of New Granada, and the Intendancy of New New Spain, so there's precedent for even small political entities wearing a lot of different names. Going across the FWL/CC border, the political entity centered on Capella was variously called the Capellan Holdfast, Capellan Republic, Capellan Co-Prosperity Sphere, Capellan Hegemony, Capellan Commonality, and finally the Capellan Confederation.
More recent sources supersede older ones, so it would appear, based on Handbook House Marik (which is internally conflicted):
Founded as: Stewart Confederation (House Marik and The Periphery call it the Stewart Confederacy, but H:HM goes with Confederation)
Renamed after Stewart War as: Stewart Commonality
Stewart Commonwealth is likely just a typo on the map - somebody copy/pasting Marik Commonwealth and forgetting to change the back half. The Liao book, for its part, refers to the Sian founding state as both the Sian Commonwealth and the Sian Supremacy (copy/pasting from Sarna Supremacy).