When I used to have a PVP server character... long time ago before I deleted the char.
Night Elf : Suddenly
Cat : Ninjas
But usually I tend to name pets based on role or purpose. Though in pvp I tend to get creative sorta, my usual was naming the pet "Karma". But I've had some alts with Pink Plainstriders named Boomstick or in one case EgoCrusher (hey killed by a pink flamingo...)
Used the spider from bloodmist isle and kept changing it's name (go go scribe leveling!): Screams, IceCream, Nightmares ( never tried but NightmareFuel was what I wanted but too long)
Wolves/worgs : Clyde, Cinders (red tint wolf from badlands), Paws, Slurp, Nuzzles
Cats: SexyClaws, Pirates, Surprise. Ninjas
Now PVE I've named bears, beetles and turtles "DaTank" or "ItankNow"
Though my favorite was a boss wasp pre nerfed size "IhateTanks" though it was mainly for friend and guild runs.. pug tanks have no sense of humor about pets bigger than some bosses (before BW was hit!)
Now looking at what pets my current worgen hunter will have and trying to name them:
Dog - Jeeves (old english butler name

) > going into stables for nostalgia (not a fan of the model)
Wolf - Boyfriend (yesh I went there .. cause I am evil)
Beetle (white) - Stormie (as in stormtrooper if it will not fit or work with full name)
got a couple others I want, but no names decided yet
(and hopefully not that bad of a necro...)