i like to wait until i have the pet for a while. See there personality and what not before naming them.
That being said, my 3 kits all have names for reasons. The two parent chins (Chico and Sophie) i had taken in, and i usually don't change names.
The first male kit my ferret found under the refrigerator. I had no idea he was born, no idea she was even pregnant. He obviously escaped his cage. Since i had no idea he existed, its amazing he survived away from his mother. I had hit the circurt breaker to shut power off to the fridge. When it came time to turn it back on, it never worked right again. We had to replace it a few days later. 20+ years old, the fridge gave its last bit of life to save my baby chinchilla. - I decided if the kit was a girl i was going to name her Amana after the fridge that saved her. However the kit turned out to be a male so i named him Houdini. Considering what happened, and some other stuff he pulled, it seems oh so fitting. - Since my mother chin was likely pregnant again by the time i found out about Houdini, i decided if one of the new ones was a girl, i named her amana instead.
She sure enough was pregnant and 3 months~ later she had two girls. One that looked exactly like her, and one that looked just like daddy and Houdini. So i thought id name the girl that looked like Houdini; Amana. And i was tuck for a name on the kit that looked just like mommy. I mentioned this to a former breeder i was talking with at the time, she helped me out a lot, and she suggested since mommy was Sophie, how about the look a like named Sophia.
I was kinda ashamed i didn't think of that lol. But it was perfect on several levels. Not only the likeness of them but one of the games i had played recently Star Ocean: Till the end of Time had a character named Sophie. You eventually run into another character named Ameena who looks just like Sophie. They woulda been twin sisters almost. - And Ameena was so close to Amana. It just seemed to fit perfectly. So the sisters became Sophia and Ameena (still paying respect to the fridge.)
Sometimes life just chooses for ya'