Her actual name is Fiona, but when she was little, I called her my "inky binky biddy baby" (I know, yuck!), and it just sort of evolved from there. I actually call her "Inga" about 75% of the time, or more frequently, "Ee." Evangelion was a natural spin-off, I guess.
Nicknames are a big part of my world. For example, I grew up being called Winnie. That was just what my dad called me, a secret identity. I went through a phase where I hated it, and then I recently started liking it again. And by recently, I mean in college, when I saw The Shining for the first time. Winnie suddenly seemed like the coolest name in the whole dang world after watching Shelley Duvall take on Jack with that baseball bat.
On the other hand, my brother wound up changing his name. He always hated his real name and the nickname my dad gave him. But one day he invented a character for an RPG--and found his real identity. He got all his teachers to call him by his new name and eventually convinced my parents to help him change it legally!
Fiona loves her name and tolerates all the weird things I call her. I suppose that Evangelion doesn't sound too bad compared to the pet-name I gave my mom: Skoonamagawa.
So if you're doing any writing, keep nicknames in mind. They say a lot about the characters who use them and the characters who created them. The nicknames I use for my family members probably show that I'm a goofball who ought to have her mouth taped shut.