She's adorable! She looks like a yorkie to me.
I don't think it's a big deal to change her name, especially if she isn't responding to it anyways. My puppy mill rescue was named Savannah by the rescue, and we changed her name to Lane.
I'm so happy you are rescuing her, and I can't even begin to tell you what an amazing experience it will be to watch her come out of her shell. Any time my Lane shows confidence I feel such a sense of pride, which is admittedly a bit ridiculous.