When we bought Morrie, who was named such by the breeder, she offered to change it for us before we got him so he would "know who he is" before he came to us, but with the exception of my mare, Angel, who came to us as "Sugar" and my first brain reaction was Angel everytime I looked at her (more like I couldn't train MYSELF to keep her old name instead of training her to know her new name), every animal I've owned gets to keep their name.