This is really interesting!
My cat, Lola, I got from a shelter in California. Her name was LaLa . She got loose and ran away before I even got her home from the shelter. I searched all over for her and was not about to go around calling "Lala, Lala" for fear of getting locked up! So I changed it to Lola. I figured it was close enough sounding to Lala, that she would still recognize it. (I finally got her back 4 months later!)
Chelsea, my ferret, I got from the shelter here in Minneapolis. She came with the name Lucy, which was the name of my very first and favorite ferret.(I figured it was a good omen) Can't have two of those, so I changed it to Chelsea since it sounded similar.
When I was a kid, we got two Siamese kittens for Christmas. We couldn't agree on names so they became "Big Cat" and "Little Cat". After Big Cat (aka Fat Cat) died years later, Little Cat became Old Man Kitty and lived to be 23 years old!
I acquired a cat from a woman I worked with many years ago. She had named the orange persian "Matilda Rose" and called her Matty. When I got her, she was very fearful and I realized she had been abused by this woman. I decided to change her name because she probably associated her name with the abuse. I renamed her Rosie from her middle name. My dad ended up with her and she had a great life with him. She was always timid but very sweet.
I rescued a ferret that was a light brown and cream color so I named him Bailey after my favorite drink!
I adopted a cat once who came with the name Spunky, but he was anything but that when I got him home. He had the sniffles when I got him so I renamed him Snuffy. Once he felt better tho, he was definitely spunky and then some! But Snuffy stuck and I kept it.