So, the first name and surname of Ryuzan Kyouko should probably be reversed.
Ryuzan actually works quite well with the naming conventions (fun fact: before his first name was Ryuji, my character had the surname Ryuzan! 流山, "flow" and "mountain"). However, it's not a Japanese given name, and feels (for want of a better term) much more like a surname. Of course, bizarre first names do exist and can be pretty much whatever you want. However...
The vast majority of names ending in "ko" are first names (Kaneko is the only surname that comes to mind, and indeed the only one listed in the
100 most common surnames).
Kyouko specifically is a well-known Japanese first name and doesn't appear at all as a surname. It's also exclusively a girl's name nowadays - your Kyouko is a male Raen, right? - what with "ko" being a feminine ending, although you have some wiggle room there since that particular convention didn't become common until the 20th century and was actually a masculine attribute in ancient Japan (though moreso before the Edo period where Raen names are devised). Either way, it would be spelled
Kyoko, since FFXIV's Japanese romanization drops the syllable-extension vowels (hence why it's "Yugiri" and not "Yuugiri").
Naturally, no character name needs to follow the conventions 100%; I just figured it was worth mentioning, since it's juuust shy of being lore-accurate.