Astro has so many nicknames. Walrus, Hippo, Wrinkle, Wrinkle-face, Lil Wrinkle, Drool Face, Drooly Puppy, Fluffbutt, and Bubs, to name the most used ones. He responds to "wrinkle!" as much as to his actual name.
I tend to only use his name for training and recalls, and it has a lot of potency. All other times, it's a nickname.
Pit is definitely Chu or Tsu always, unless someone asks me what his name is. Chu is the "formal" name I use for getting him to listen, Tsu is for tha sillies and usually comes out like "TSZEEUUU!!" I don't know the last time I've addressed him as Pit.
Navi is some variation of her name said in the most obnoxious way possible. "AUHHH! IT'SA NAAUUUVUHHHH!". If I'm talking to her seriously, her name sounds like No-aeh kinda, I guess.
Zero is Zero or White Doggy - name courtesy of the neighbour kids.
Fable goes by 'Beauty' about 70% of the time. When my friend met her for the first time she commented on what a beauty Fable is, and I have called her that ever since. Another nickname is 'Fabes', which popped up because sometimes I think 'Fable' is too long.
I only call my guys by their "given" names in public (and their registered names if they've done something they shouldn't. Well, except Holly because there's no way to sound stern while saying "Hotsy"). Because, you know, they'd be embarrassed by the long list of cutesy pet names they get at home.
Yes, I do, for the most part. I usually do for everyone though. A lot of people go by nicknames, for instant, that I know, and I still usually call them by their actual name. It's just how I have always done so, so!