This is speaking of modern Germany. Historically there was no "Niedersachsen" and no "Sachsen-Anhalt". There was the Prussian province of Sachsen and there was the Electorate of Saxony, in German "Kurfürstentum Sachsen". Then there were some more Duchies with the name "Sachsen" in themselves that are mostly located in the area which is today Thüringen, such like "Sachsen-Coburg-Gotha", "Sachsen-Altenburg" and some more. So basically, to get a clue which area name is the one to use, you need a very exact place and additionally a quite exact time period, because the name sometimes changed quite often.
