This is a little complicated to explain, but if your event is bullet on collision with player > player destroy, then you need sub events to compare the bullet variable back to the shooter. Sub event would be something like pick player(shooter) where name = bullet.name (the variable that you mentioned to track the shooter).
But there is a further problem, because you already narrowed picked instances to the player who was shot so 1 player, you need to open up the other players again to be picked, so first you need a sub event like system pick all players, then a further sub event with the above logic about using the bullet variable
OR instead of using these sub events you can call a function that inside has the logic for picking the shooter and incrementing their variable and also does not have 'copy picked' enabled.