Well, my dog is named Voltaire which is absurdly pretentious, I think. I let my then BF talk me into it, and I kind of wish I handn’t. I was thinking Barkly or Bowser, but there you go.
FWIW, everyone (including me) calls him Boo. Boohini, if we’re being formal. He’s only Voltaire if he’s being naughty, which isn’t very often.
Mine is Leonardo. He was named after da Vinci, which I suppose is a little pretentious, and DiCaprio, which is less so. He is mostly only Leonardo when he is being bad. Most times he is just Leo. (Took him less than a day to learn the difference. He’s a smart cat.)
I’ve got Mikey, the Dachshund-Corgi mix. He’s fourth-hand and came pre-named. I have to tell people that because my name is Mike and they all think I named the dog after myself. (Who does that?) I got him from somebody who got him from the pound and I have no idea why he was ever given away. He’s wonderful.
My other dog, a black lab/border collie mix, is named Banjo but called Pooter due to some intestinal issues.
The cats are Miss Kubota, aka Bobo Kitty, who was found on a construction site and the twins Basil and Sybil. They were going to be Polly and Manuel but they are much too Fawlty for that.
I am a dirt-poor high-school drop-out, but my pets have relatively high-falutin’ names. Kea, Ferdinand and Fairuza.
I like to give my pets ‘people’ names but choose those that are more uncommon, old-fashioned or foreign. I do take the meaning of names into consideration. Kea means ‘white’ in Hawaiin, Fairuza means ‘blue’ in Romanian - they are white and blue-gray, respectively. Ferdinand is a Germanic name meaning ‘brave’, basically, which my Ferdy was very much not when I got him. He also reminds me very much in looks and personality of Ferdinand the Bull, which was a favorite book of mine as a child.
I asked our pets, **White trash Kitty **and Redneck Dawg, and they said this theory was baloney.
Cats:
My longest-living cat (21 years), female tabby was called Minette, which is as generic as you can get in French. Her son was called Pussy (named by my 4-year-old at the time, obviously not the adults’ choice). We kept a friend’s cat, Bigfoot, for 7 years, and another friend left his two cats Knickers and Sam to live with me about 10 years, until their death(s).
After that lot had shed this mortal coil, we got Ishtar. By then, my son was studying Classics and Archaeology, so I let him choose the name. Then we rescued Athena-Gaia (I called her Poupoune) and Wotan.
(shortening long story)
We now have Loki (a crazy mischievous long-haired black tabby) and Ziva, a brilliant calico (she was a rescue and her foster had named her).
Dogs:
Mohican (black Lab)
Sarah Bernhardt (Saint Bernard), we called her Sarah.
English Mastiff called Tarzan.
We’re definitely not upper middle, probably right in the middle middle.
My current cats go by Rupert & Ollie, but since that is short for Prince Rupert of the Rhine and Oliver Cromwell, I’d guess that counts as pretentious :D.
Those are actually the worst, but all of my pets reaching back to childhood that I have named myself have “human” names, with the exception of Huckle the cat - Sandy, Veronica, Hank, Max, etc…
My class? I dunno. I’ve never gotten a good fix on that. I consider myself to be something of an outlier in terms of social class boundaries. But I do make a good income and am well-educated in a very general sense, so I suppose it perhaps falls into line with that.
My first cat’s name was Tabitha Twitchett, from the Beatrix Potter story. Does that count?
Current cat is named Miette Mittens.
I would say I’m upper-middle class.
Over educated middle class with cats named The Shoe, Magick (named when I got him), Mr. Spock, Yogi (named when I got him), Lt. Cmdr. Jadzea Dax, Cricket, Sugar Magnolia and Leroy Jethro Tull.
Eight cats?!
Your nick is well-chosen. 
We once had a dog named Pheyedeaux. Common name, pretentious spelling.
My cat is named George. I named him in honor of several different historical figures named George: George Clifford, 3rd Earl of Cumberland, King George V of the UK, and also George Washington. Knowing that, it may sound pretentious, but nothing about his name alone is pretentious.
We used to have a purebred Golden retriever, who we named Sparky. We had his lineageon a printout and his ancestry boasted names such as “Brandy Golden Britches,” “K-C Winn’s Torah Topaz,” and “Jason’s Golden Conquest.” We decided to retrofit a “fancier” name and started claiming that “Sparky” was short for “Golden Sparkules of that ilk”… which was us pretending to be pretentious, which is close enough.
Our cats have pretty unpretentious names: Pixie (she has big ears and a tiny little elf face), Cory, and Ronon (named after a TV character).
Our income/class is pretty low at the moment, so I guess our cats’ unpretentious names would reflect that?
Working class background:
Had two dogs once who were littermates. One was called Praxiteles and the other Dirt. (They also answered to Maxine and Gertie and collectively to ‘The Doots’).
Other assorted pet names over the years included The Boods, George (female), Doug (female), Mr Rednuts, The Ratbag (also called Beans), Pup-a-noodle, and Tim.
Here you go: Max’s webpage
and Dirt’s
We have Gunner the Great Dane, Oreo the Pomeranian, and Carson the Shepard/Chow. Had a cat once named Joey and one named Gary. I did however want to name Gunner Felix instead. Wife vetoed that idea.
I named my cat Feather (her name at the shelter was Patches - not very original for a calico kitty). My husband named his cat Max (a girl kitty). I don’t think there’s much pretension here.
ETA: If we get another cat, though, we’ve planned to name it The Magnificent Fangmeyer. That might be a little pretentious.
I worked in cat rescue for many years and had a habit of taking my work home with me; all of my current cats are rescues.
My lab is called Jana, after the poet Jana Beranova, because she wrote:
“Als niemand luistert naar niemand vallen er doden in plaats van woorden”
Literally:
“When nobody listens to nobody, death will fall instead of words” (implying people will die instead of speak)
Sorry…
My cat was called Tabby though 
'cos she was a tabby cat! And the next lab will be James James Morrison Morrison Weatherby George Dupree, after the A.A. Milne poem.
I’d love to name a cat Pangur Ban, after this poem:
Written by a student of the monastery of Carinthia on a copy of St
Paul’s Epistles. - dated aprox. 9th century AD
Translated by Robin Flower
Original Irish here:
Our cat was named Max.
On the other hand, we own a couple carnival-won stuffed animals named Princess Plumperpants and Commodore Frogenstein.
I once owned a pair of newts named Behemoth and Leviathan.