I see a lot of pet names in my line of work (about 500-700/day), and am forming categories for them. The following is an unscientific as possible.
There are a lot of names based on the animal's color (Blackie, Patches, Snowball*), which somehow strikes me as a cliché which that classic cat name, Kitty, eludes. I haven't come across any canines named Dog but have seen a couple named Kitty.
Macho female dogs such as boxers and pit bulls are often given ironically girlie names such as Baby Girl, and a dog named Killer is either a pit bull or a chihuahua. For a while I thought that Bella was reserved for non-ironic use (especially appropriate for golden retrievers), but then ran into a spate of German Shepherds and boxers sporting the name. However, Isabella is reserved for small, pretty dogs or for cats.
In the unexpectedly popular name category, hoards of female dogs come when they hear "Hannah", and Scooter is seen as eminently suitable for both dogs and cats of either sex.
A huge number of Americans think highly of themselves as pet owners and name their dogs Lucky. Classic people names such as Molly, Maggie, and Sammy are probably in the top ten. There are occasional literary references, such as gray cats named Gandalf, but not as many as I would expect, and so far none from books which were not also made into movies (Mr. Darcy can hardly be escaped). And one elderly lady from California sent in information to license George Clooney and Brad Pitt (the Siamese and short haired cats) but forgot to send any money. George W made an appearance, and a few chihuahuas have been named Paris.
If I ever have to sue for emotional abuse, it will be over the enormous number of pets with sickeningly cutesy names, but I will leave that shame for their owners and not retell it here. There is also a less alluring subset of the population which gives their pets names like Stinker and Fart, and if I could tell them a thing or two it would all center on how words have power over us and influence our emotions and affections, so they probably love the animal less than if they had given him another name.
And so far my favorite name for a cat was Potlicker and for a Jack Russell Terrier, Chase Little Foot.
*Although these names are also gives to animals of different coloring but not in a way suitable for irony (such as the brown dog named Blackie), which boggles the mind.