All of my original pets (from 2001 or so) have TERRIBLE names because I had no idea what I was doing and took whatever abominable string of numbers and underscores Neopets unhelpfully suggested I append to my original (taken) choice. These include Angel_Rules_2001, Ally_Anna33, Sigma123_2001, and Zena1305. Yikes, but... y'know. It is what it is. I'm too attached to them to ever do anything about it.
All of the names of pets that I created post-2001 (which really just means 2020ish to present, lol) are very carefully chosen and have special meanings. I like to either find a unique but related word for their eventual appearance (color/species), or combine a few until I get something that sounds like what I want.
Rivulett, my Maraquan Lutari, is just an alternative spelling of Rivulet (which was already taken), meaning "a very small stream"
Samsanthea, my Island/Christmas crosspainted sunflower Kau, got her mashup name from the Hebrew "Samson", meaning "like the sun", and the Greek "Thea", or "goddess". This one is also extra fun because I have synesthesia and the colors of all of the letters in her name - it’s a very autumnal palette - are present in her customization!
Amplexicaul, my Woodland Techo, is a term that describes a specific type of leaf; fitting, then, for a leaf-footed gecko!
HedleyKow, my lab rat (currently a Pastel Bruce, which is actually super cute), is named after a mischievous faerie tale elf whose most notable quality is shapeshifting to play harmless tricks on unsuspecting passersby; again, perfect for a pet whose entire purpose is to let me play around with the lab ray.
ETA Primordhia, my new Chomby as of Chomby Day, whose name comes from "primordial" for obvious reasons; I think I'll eventually paint her Relic!