The Names forum would likely get you the best help, but I can suggest a few of my favorites.
Fenrir for the wolf.
Myst or Mysty for Ban'thalos
Hela or Tsuki for Loque.
Fireass (funny, non-serious one suggested by a guildie) or Firestorm for Solix.
Fluffy (Harry Potter reference) for the corehound.
Part of Dark Magics, lvl 25 Horde guild, casual, helpful, don't raid, mostly help people and hunt pets.
Part of Dynasty, lvl 25 Alliance guild, casual and hardcore (your choice, no one forces you to raid, but you can), very helpful
Come on over if interested (Runetotem US, Horde name Sarantha, Ally name Ellysetta or Valeraud)
The burns of a fire may heal with time but the burns from our love will never heal, even as the years pass on
{My Magistream Keep}{My DA}{My DC scroll}
I always liked Gemini for the blue core hound, I have him named that on my hunter Styxx.
Hmm.. Loque is always a tricky one to name, my main's was named Loki for a long time, but that name is dirt common for Loques on my server. My Loques are named Fai and Rowan, after characters, and the third is named Sidhe.
Solix.. I never went after that one really. Sunkist perhaps? My main had a red lava spider named Pyrotechnic for a bit there.
My Banny is named Hatsu, which means "first", as he was the first to appear on the server and I managed to snag him because of these lovely forums and nobody else knew how to get him when he first showed up. I was really frighted about it, a DK kept trying to kill him during the tame. Ah.. He always reminds me of a rave when he fights, all those pretty flashing lights (I actually never intended on getting him myself, it was a bit of a whim and a self challenge-and now he is right up there with Loque as my favorite pet in game). I plan on getting him on my next hunter I get to 85 when I can and naming that one "Rave" just because of thsoe flashing lights of his wingtips in combat.
I cant see the color exactly of the wolf in your screenshot... though Pollux has always been a fave pet name for the fluffy wolves for me.