Why couldn't you just print "Player 1, press your buzzer" and then use a loop to check all four of the buzzer buttons to see which one is pressed? Then you could place the value of the number [the joystick fire x (number)] of the buzzer that is pressed into an array. You would need to do error checking in case two or more of the buttons are pressed at the same time.
Then simply input their name into a string array [i.e. input "Enter your name: ";PlayerName$(1)]. Do this for all the players and you are good to go.
I would use separate arrays to identify the joystick fire x(number) associated with a particular player and the player's name. You would just use the same value to associate them both. Player(3) would correspond to PlayerName$(3), etc.
I hope this answers your questions.
LB