Restricting access to a quiz can be done with groups. Name the group Quiz 1 and then anyone in this group would have access to Quiz 1. When John Smith needs to take Quiz 2, he can be moved to the Quiz 2 group. Here's more info on Groups in Moodle: https://docs.moodle.org/311/en/Groups

Create the groups and restrict access to the quizzes for their particular groups. About halfway down the link above are the steps to create groups and then restrict access within the quiz settings.