Upper Saxony
It was particularly to distinguish the lands from 'Lower Saxony', a concept which arose later in popular usage (though never enforced) as a term for the original Saxon lands in north and west Germany (where Low German dialects had spread), in what is now the state of Lower Saxony, as well as the adjacent Westphalian region, Holstein and the western part of today's Saxony-Anhalt north of the Harz range (Eastphalia).
Herzogtum Lauenburg
The district Herzogtum Lauenburg is named after the medieval Duchy of Saxe-Lauenburg, which was one of the remnants of the original Duchy of Saxony. The Duchy of Saxony was partitioned in a process started in 1269, nine years after in 1260 Albert II and John I had succeeded their father Albert I of Saxony. In 1269, 1272 and 1282, the brothers gradually divided their governing competences within the three territorially unconnected Saxon areas along the Elbe river (one called Land of Hadeln, another around Lauenburg upon Elbe and the third around Wittenberg upon Elbe), thus preparing a partition.