Puppy: Because I love dogs, someone nicknamed be this. I liked it. So I kept it.
FaBa: Well... long story with a long explanation. To shorten it, a being with goop in its mouth's way of saying "Father *insert my real name here*"
Baby: I don't... really... know? My guess is that someone took my name, made the first two syllables into a nickname, then warped that more. It's really odd, though.
That math kid: I like math. A LOT. I'm fairly good at it, too, so some people started calling me this. I actually sat with this one kid last year in math class, and when the teacher said, "work with your desk partners", I looked at him, and he flung his chair backwards, slammed his binder on the ground, and shouted, "IT'S NOT FAIR!". Probably because a) I'm a lot better at math than he was, and b) I hate working with other people, so I just hurry ahead and wait for them to catch up when I'm done.
I think that's it!