If you want to rename your dog, go right ahead.

While it may take an older dog a while to figure out what you mean, he’ll get it eventually. Dogs don’t internalize a name the way we do; they don’t identify themselves with that particular combination of phonemes. They simply understand that when you make a certain sound, it means something is happening that concerns them. Thus, you won’t hurt his feelings or cause identity confusion, although it is true that unless you really can’t stand your dog’s former name, it’s probably easier just to stick with it.