I don't use common human names. When I'm talking about my pet I want it to be clear that I'm talking about an animal. Otherwise, it can be awkward. If you heard me say that I took Billy to the park. You'd assume I was talking about a person, probably a child. If I said we played frisbee, you'd think that's perfectly normal. If I then said that he chased a squirrel, you might start to question your original assumption. You might not reject it completely, but you'd begin to doubt it. If I then said that he pissed on every mailbox on the way home, your initial shock would give way to a relieved laugh as you finally realized that Billy is a dog. Better to avoid this type of misunderstanding and just give your pet a name no one would name their kid.
My current snake is named Wiggles after the Australian children's program because he's an Australian Children's python. My only other snake was a BP. I named him Fonzie after the Happy Days character because he was also very cool. I suppose Fonzie is technically a human name, but no one would name their kid that anymore.
Or you could make a game of it. When we named our guinea pig, we spent a week writing potential names on a white board. At the end of the week, we'd vote. The top vote getters would advance to the next round until we finally settled on a the name Chewy. If it's a family pet, that's a good way to get everyone invested in it's care.
So, definitely not random.