Ummm.... but latin is still being used a lot and carolus magnus would be the same for each. Moreover the dutch speaking parts of his territory are likely to use karl de grosse ... or something for both. I think the distinction yourre trying to make only works in french and english.
First of all great TL!
In Dutch Charlemagne is known as 'Karel de Grote', however I doubt that we would use the same cognomen for a successful ATL Charles ''IOTL the Bold", especially since Charlemagne was our ruler too.
Alternative kingdoms for the Burgundian dukes would have been Lotharingia, Frisia or an elevation of the duchy of Brabant.
Burgundy could work too, this creation would ''migrate'' North though, most territories, which belonged to the kingdom of Arles would have been detached from it (not Franche Comté) and other regions (mostly in the Low Countries) would have attached to it.
An OTL example is the duchy and later also electorate of Saxony, which gradually moved eastward in the HRE.