To accomplish this change, you should use two arrays: one to store each player's score and the other to store each player's name. Depending on your original design and how you implement the changes you may need to re-write some of the methods. Remember to draw pictures of your arrays and to use those pictures to understand what you want to accomplish.
Try to make your changes incrementally rather than attempting to fix the entire program all at once. This may require that you temporarily comment out various sections of your program and implement your changes from the the bottom-up just as if you were writing it from scratch.
Remember to work on it every day and to enjoy the process!