BlameThePixel!

Ahem:

Lightside's God = The Concrete Donkey.
Darkside's God = Buffalo Of Lies
Brightside's God = None. Brightsiders follow absoloutly no code, unlike all the other sides. They consider themselves to be smarter than everyone else because of this, hence the name Brightside.
Greyside = None. Greyside is actually one of the lesser sides, along with the much lesser (and also Godless) Sewerside and Flipside. Sewerside is self-explanatory, though I don't know what Flipside represents.

The Angular Wooden Giraffe is not the offical God of Greyside, but they represent the same thing. Also, the AWG was implemented, as a map in WWP. It favours Lightside and Darkside play, and is what the entry in the Wormapedia is referring to, not the picture it shows.

As for God names, I've never heard of such things.