I wonder though if she had herself called Katie by her holo-lover as a part of playing someone not quite herself.
I just took it as a more familiar form of her name that she would never allow anyone on the ship to use. "Kathryn" is a pretty formal-sounding name, at least to my ears.
Guy Gardener wrote:
Katie, not Kathryn was her character name in the Fairhaven holonovel.
PATTERSON: You're late.
JANEWAY: Sorry, sir.
PATTERSON: What's the threshold of the H-two molecule?
JANEWAY: Fourteen point seven electron volts.
PATTERSON: Third brightest star in Orion?
JANEWAY: Viewed from where?
JANEWAY: Gamma Orionis, or Bellatrix, if you prefer the original Arabic name.
PATTERSON: Not bad. Now, give me a hug, Katie, that's an order.
JANEWAY: I wasn't expecting a pop quiz.
PATTERSON: Just wanted to make sure all those pips haven't made you forget you're a scientist first.
JANEWAY: How could they? I still have nightmares about your fractal calculus final.
Well, some Admiral no-one from her past could get away with calling her Katie.
The DaVinci hologram would have been talking in Italian unless Janeway instructed it to speak in English, but the Universal translator would have wrestled what he said into English.
Maybe her name was not translated from the original Italian?
I'm guessing Admiral Patterson was probably a special mentor/teacher Janeway had? Possibly someone who might have been friends with her father, and therefore a family friend? Speculation, I know.
"Caterina" is an Italian form of "Kathryn" - at least according to The Borgias
It's not so unusual to use a foreign form of someone's name when otherwise speaking English. My RL middle name is the Swedish form of an English name, and I'd never expect anyone to refer to me by the English form. And I spent over a dozen years in the Society for Creative Anachronism. My persona in that organization is Norwegian. Even to this day there are people who know me only as "Freydis" and would never call me anything else. I answer to that name as readily as my legal, given name.