I dunno. I'm inclined to believe that Katherine is Kitty, and that Kitty was just a nickname of sorts, that she outgrew.
In the library in MaW4, when you're forced to dig around looking for clues as to Katherine's identity, you read through several volumes: Volume 3 documents Will and Iry Smith, from MaW, and the establishment of the Hunter Academy (first generation presidents); Volume 4 documents the moving of the academy to the old castle by Sheryl Winston and her husband (second generation presidents); Volume 5 discusses an unnamed female president of the third generation and the Academy falling into ruin, protagonist surmises this to be Katherine (and later gets confirmed when he speaks with Phyllis); Volume 9 MaW3 which is the generation immediately before MaW4.
Further anecdotal evidence: When protagonist mentions he has a Syrine (or however it was romanized) member in his party Katherine remnisces about when she fought with a Syrine. Katherine mentions Carl reminds her of someone she once knew (I'm assuming this to be Cliff).
My conclusion. The "Carl" that Cliff is a reincarnation of is not the MaW4 Carl. That would be impossible, due to timeline. MaW4 Carl may or may not be a reincarnation of Cliff and previous Carl, though when you talk with Phyllis it's revealed that he's definitely descended from them. Kitty could have possibly grown up enough to take charge of the Academy after Cliff and Sheryl pass away, as unless my memory fails, she was only so young due to having been put to sleep, and though the Succubus are a slow aging race it wouldn't be that out of the question. Also, while only seen briefly, there are flash-back event cgs that are pretty damning evidence as well. The final nail in the coffin would be that, while hunting around the game archives for said cgs, I stumbled across further evidence. The internal script filenames refer to her as Kitty. While I normally disregard such things as conclusive proof on their own, as additional verification I don't see why they shouldn't be considered.
(I am also quite curious about H_ReinaLeana.scr is this an unused twincest scene?! Or just a case of odd filenaming. A peek:
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I do not remember this in any scene in the game.
There were no hidden additional CGs obviously. Though, there were some strange other extras in the cut-in section for battle combos... Maybe this has some relation to all those weapon types that you can find, but nobody in your party is able to actually equip?)