Don't really have nicknames. But we did get a second cockatiel when one of my dad's friends found it on his farm. We didn't get a name for it at first but it ended up being referred to as "the fat one". Weird thing is it wasn't fat.
Dog called Daisy - Dais, Daisy-may, Beastie (also applies to all golden retrievers), Pest, Bugger dog (more affectionate than it sounds!) She also responds to 'Oops' as much as her actual name because we used to say 'Oops-a-Daisy' when we dropped something edible and kind of lost the end over time.
Socks: Moxy, Teg, Montegro (Don't ask, I don't even know) Big cat, Moxy Girl Little Cat: Cat-rat, Little rat, munchi (She's just a mini me of socks really, which is why she's little cat)