Normally you have to sign a form before visiting which says that this particular agent is the exclusive agent for a particular unit, they will actually list each place individually. If another agent offers you the same place just tell them to leave it off the list.
Should it happen that the same place ends up on another list just tell them once you realize that you have already seen the same place, I am sure they would be willing to strike it out; just tell them before you decide to rent through your other agent to avoid any conflict.
Sometimes you may not want to sign or the agent may not ask, in which case it would be your choice which agent to use eventually if you decide to rent a place, and without the agreement other agents won't be able to charge you (if they ever learned who actually rented the place).