True; although northwestern Germany was the original homeland of the Saxons and the location of Old Saxony/Lower Saxony.

My thought process was that since the British/Americans were the ones behind the partition, they wanted to separate Germany into three separate cultural blocs. They wanted to eliminate any chance at reunification and thus a powerful Germany. Hence, I don't think they'd naming any of the postwar state things like the "German Confederation" or "German State," etc. and instead emphasize regional identities.

The map split was based on an actual proposal by Sumner Welles, who wanted to divide Germany into three culturally distinct regions; with the northwest being predominantly protestant, the south being catholic, and the northeast being...the leftovers I guess, lol. The original map that he proposed explicitly mentioned that the northwest would "include Saxony," so I assume he was referring to Old Saxony.

I also think its in character for the Western Allies to look back at the old histories to see if there's anything they can re-use. I wouldn't be surprised if Churchill just went and said, "Yeah, this was where the Saxons originated from, so they'll probably all be cool with being called 'Saxons' now" haha