Hanoverian is not really a good name, simply for being completely anachronistic in 1444 and up to the 18th century, and because even after the creation of the electorate of Hanover, it only refers to the territory of that political entity and does not have any linguistic, ethnic or cultural significance.
It is in no way accurate for the many territories in North Germany that were never ruled by the Welfs.
Westphalian, on the other hand, is certainly not a Napoleonic invention; Westphalia was one of the four subdivisions of the ancient Duchy of Saxony which was much larger in area than what later became the Duchy of Westphalia held by the Archbishop-Electors of Cologne. That said, it is not a good term for the area covered by the culture in EU4, because it represents only one quarter of it.
What exactly are the "own problems" that calling the culture "Low Saxon" brings? This is what this area is referred to as linguistically and culturally, and it is a name that still lives on in the Bundesland of Niedersachsen (Low Saxony) today. Please do not say that the problem is people being confused because, duh, Saxony is elsewhere.