Sometimes they end up in shelters, and most of those attach names to their strays these days (used to be just a number.), but they rarely know them yet, so I choose what I prefer in those cases.
But, like you, if a dog comes with his/her original name, I keep it. That's how dogs like Maggie the Australian Shepherd, and Pepsi the JRT got their names. I just didn't change them, because they knew them.
I like that you have been able to make small changes that retains the sound of their names, but still improves on it for you.
Love All Life, Thank You For Posting! :)