Having owned several animals who came from abusive situations, I totally agree with a name change, no matter how old the animal. I think anything that can disassociate the pet's memory from a horrible past life is for the best.
I also think that dogs adjust quite well to name changes and learn them within a few days to a week...and learn that when they hear their new name, that it's a good thing! Whereas in the past, hearing their name...was probably connected to intimidation or even violent experiences.
Also, if you just took in a new pet from an abusive situation...Kudos! As I've said, I've done this several times and never regretted it.