Concerning Castlevania and the name Belmont, it is certainly not a French name, because its katakana transcription is "berumondo", whereas in French, the final -t of Belmont is not pronounced and it would certainly be written as "berumon".
Personally I never pronounted the "t" of Belmont in any Castlevania game, as a french native. So either the japanese transcription is incorrect, or the latin transcription is incorrect. I'd bet on the former, japanese guys were looking at french names, and transcribed it in katakana without knowing the final "t" is not pronounced.
I'll also add that before 1860, the border between France and Italy (or rather I should say - the border between the French world and the Italian world - Italy wasn't founded yet) were not properly defined. There was an independent country named Piedmont-Savoy
which was part of what is today southestern France and northwestern Italy, and it was bilinguial. Most people spoke hybrid dialects that were neither french nor italian, but sort of in-between. The modern Italian state of Aosta valley is still French sepaking, although it has been vastly italianized during the XXth century, particularly under Mussolini. All place names and most people's family names are in French there, even if most young people have Italian as a mother language. (Only in more remote places - and this valley is full of them - people still speak French or a French dialect at home, but before WW2 everyone did).
Some villages in western Piedmont just next to France are in a similar case, I guess, but they have been italianized more quickly because they were not part of an unified french-speaking region within Italy.
Again, since the games are supposed to take place in Transylvania, the name should be in Romanian, Hungarian or German since those are the 3 ethnies who populated the country between the middle ages and the second world war. Also family names appeared between 1200-1500 BC so earlier Castlevania games heroes shouldn't even have a famiily name at all.
EDIT : Also, most family names in europe were not required to have one precise orthography before the end of the 19th century or the begining of the 20th century. The concept that "it's wrong if it's not written exactly like that" is fairly recent in comparison to the history of family names. So having an orthography oscillate between Belmont, Belmond and Belmondo randomly actually makes perfect sense in regard to real life.
I just had pizza.
Even if pizza is an italian dish, it was popularized by american-italian and not by italian-italians, so pizza is actually more from America than from Italy in some sense.