If your name is on a quit claim deed with right to survivorship... once the other person passes away... do you have to put that deed in your name?

You don't have to put it in your name but you should. If you don't put it in your name now, then when you go to sell the property you'll have to provide the death certificate for the other owner who passed away. You're better off having the executor of their estate issue a deed in your name now.