If he's COMPLETELY mad, maybe his reason for "blue pets" can be insane, too.
"Blue reminds me of soup."
or
"My favorite pair of socks was blue... *sighs sadly.*"
or even
"BLUE IS THE OPPOSITE OF BLOOD. *grins crookedly.*"
A couple of those pets look a bit more green than blue, though--particularly Jadefang--but for the most part they're a nice-looking set

You might want to be wary of mentioning in your RP itself why people do or don't want to hang out with your character, though; if you're RPing on a Roleplay realm, it's usually best to stick to the character himself and his personality, and let people react how they will (unless you mean fictional friends!).
As far as names go, I'd almost be tempted to call all of my pets the same name, probably something wacky, if my hunter was nuts. "They're all Box. Why wouldn't they be Box?" Otherwise, going with the blue theme might be cool.
From
Thesaurus.com:
azure, beryl, blue-gray, blue-green, cerulean, cobalt, indigo, navy, royal, sapphire, teal, turquoise, ultramarine
Or, you can name them all colors that are not blue, like Red, Violet and Rainbow. Umber, Scarlet, Copper, Sandy, Penny, Brownie, Sunshine etc are other non-blue, color-related names that come to mind.
Good luck--I love your idea, and you should post screenshots of your crazy hunter if you get the chance!