Or possibly the KoS gets Westphalia, while the Rhineland (at lest as far as the Moselle) goes to the King of the Netherlands (istr a map giving this as one ot the proposed boundaries for the KotN). This has some interesting butterflies, since if the Catholic Rhinelanders join in the Belgian revolt, we probably get a "Belgium" extending all the way to the Rhine, and having three communities, Walloons, Flemings and Germans, rather than two.
"Austrasia" or "Lower Lotharingia" strike me as possibilities. Alternatively, it might just be the Kingdom of "Aachen" or "Cologne" depending where its capital city was. Or perhaps its king might want to call it "Lower Saxony" for sentimental reasons.
The kingdom of the Netherlands might end up with some territories ((parts of) Cleves, the Rhineland), but it already got a lot with the Southern Netherlands, so this isn't going to be much and the most likely outcome would be similar to the OTL 1815 Dutch Borders.
Or know that I think of it, the title of Saxony actually had migrated to the east, Westphalia was a part of the (historic)
stem duchy of Saxony; so they just as well could have called their new kingdom the kingdom of Saxony. Or to put it differently, the kingdom of Saxony never ceases to exist, but the kingdom of Saxony is given a different territory; Prussia gets the entire
before the congress of Vienna territory of the kingdom of Saxony (most of 13 (green and yellow) on the map) and the king of Saxony is compensated with (all of
or at least most of) the Rhineland (12) and Westphalia (16) (the OTL post congress of Vienna Prussian provinces).
Perhaps the king of Saxony is only punished with this territory swap and so much with an actual loss of territory, since this kingdom will (just as the kingdom of the United* Netherlands (*= never a part of the official name of the kingdom)) have to act as a buffer state against French aggression. Although some small part of the territory could be given to neighbouring states.
In the case of the Wittelsbach option the king of Bavaria probably would have to (be forced to) trade Bavaria (which under such a scenario would become Austrian),
with the exception of the Bavarian Palatinate** (this part of the OTL kingdom of Bavaria is separate from the rest of Bavaria and it borders the Rhineland), for the (entire) Rhineland and Westphalia.
(**= not the Upper Palatinate)
(Found on Wikipedia)