
I always give my rescues new names - new home, new start, new name. They have all learnt their new name really quickly. My latest rescue has had 3 names in total - the one he had on the farm, the one given to him by the rescue and used by his foster home and the one I gave him when he came to me.
I find they learn their name really quickly - the same way as a pup gets used to its name. Mine also have other names that I call them by and they all respond to their own fun name too.
I currently have three rescue dogs and none of them have their original names.