I don't think anyone outside Konami really knows, though I'd be happy to be proven wrong on that one. At the time not only were game credits poorly kept, but in many cases they were purposefully obfuscated. As I understand this happened for several reasons. One was that game companies in Japan didn't want other companies to poach all their talent, so they forbade development teams from putting their actual names in the credits, or so I've heard. It would explain the prominence of nicknames and such in the credits sequences for many old Japanese games. Such as the credits for Castlevania 1 being made up of puns on famous horror movie actors. Another reason is that working in games wasn't very prestigious, and some Japanese devs might have even been ashamed of it back then. Plus just the sad fact that corporations usually like to keep any ideas of creator credit and ownership to a minimum.
If I had to guess though, I'd say the name Castlevania probably came from someone on a localization team or a marketer. As for which came first well, the MSX game "Vampire Killer" (just called "Akumajo Dracula" in Japan as well iirc, though it was a very different game with many of the same art assets) was released in Europe in the same year that "Castlevania" was released in the west, though last I heard there was some disagreement about which was released first. Meanwhile the "Akumajo Dracula" arcade game that came two years later was released in the west as "Haunted Castle". So I think it's safe to assume you had several different English language localization/marketing teams coming in after the fact, and not really talking to one another.
I always assumed "Castlevania" was the name of the castle itself. SotN's intro refers to it as such.
Yeah that's got integrated into series canon to some extent even if it wasn't the original intention I think. And it makes sense when translating text from Japanese to English since Akumajo Dracula means "Devil's Castle Dracula" or "Demon Castle Dracula". I seem to recall IGA tried to have some of the less Dracula-centric handheld games branded as "Castlevania" in Japan for this reason, and some of the hardcore Japanese fans gave him hell for it.