I think this would be better suited for Chicken Smoothie Discussion, I'll repost my answer there if it ever gets moved.
But I am glad someone made a pet name thread! I love picking out names for each one of my pets. I try to name them after what they look like.
Pet's name: Cygnus
This one is Cygnus, after the constellation on it.
Pet's name: Can't Help Myself
This one is named after the robot art piece that constantly tries to clean up its spill. Idk if this one was specifically designed after it but it reminded me of it.
Pet's name: Other Father
This one, with the orange and the buttons, reminded me of the Other Father from Coraline, so I named it accordingly.
Pet's name: Error
With the pixelated and then "fixed" pets from the Internet Event, I named the faulty ones as different types of problems, and the "fixed" ones as antivirus software lol
Pet's name: McAfee
Pet's name: Radiant
This pet reminded me of the Charlotte's Web game on the GBA because of rat and crow, so I named it Radiant, which is one of the words you can spell out as you play a level.
Pet's name: Yum Spahetti
The misspelling on this one is intentional. I was looking through an old email address and found an email from Toontown Online where I made my username "yum spahetti" and I thought it was hilarious. So I named this snake that, which is good because it's a spaghetti snake!
Pet's name: Give Me the Formuoli
Spongebob quote involving ravioli lol
Pet's name: All That Glitters Is Not Gold
This one has an interesting story behind it because I randomize pet names when I adopt them, and this one came with that name on the first try, so I kept it! It suits him well!
Pet's name: Dr. Quack
Named after the doctor on Webkinz World
You get the gist. For other pets, I sometimes just use the name randomizer, or I pull names from the name documents from the US Social Security website. There's a file you can download filled with millions of names from 1880 to now. Other times I randomize the names but then change a few letters to make a new name. I give each pet of mine its own unique name that suits it. Pets still growing or for trade usually just get randomized names though.