There's so many ways to name pets...it's really up to the owner. Many like to use favorite book or movie character names, or wait until an animal shows more personality, name them accordingly. You can use a name dictionary- with most of my snakes, I figure "exotic pets" should have exotic names, so I've looked up names with relevant meanings- I prefer to give pets names that won't be confused with human names (not that snakes "come when you call them", haha). And then there's all the other somewhat frivolous pet names like "popcorn" or "pickles", etc. Almost endless possibilities.
My dogs have always been "second hand" (nearly all from shelters & always adults of varying ages) so if they came with a name they knew, I don't change it without good reason. A good reason would be like a brown ("red") Doberman I once had- she'd been terribly abused by her previous owner & the law took her from him, so in her case, I totally changed her name so as not to remind her of her past. She became "Murphy" (Brown, like the sit-com); she soon learned it & would wiggle from nose to tail when I lovingly said her name. She was sweet & I could do anything I wanted with her, but she never warmed up to men (due to her awful past) so I always had to muzzle her for the vet- I couldn't blame her one bit. My current 2 dogs don't fit the names they came with (IMO) but I kept their names as I had no good reason to change them.