From a methodological point of view this is a very important issue, because when there is no correspondence between the experimenter and the subject who is performing the task, the results are not meaningful.
From a psychological point of view this is a first explicit basis of mutual trust. It looks so simple this point, so trivial, so needless, but it is very essential, because for both parties involved, it creates a common field of meaning. No game can be played without this basis.
From a research point of view this opens a wider perspective in a sense, that it does not matter whether the subject calls the person on the slide Jan, Piet or Klaas or "A", but what is of importance here is that the subject consequently repeats this answer over the trials in the task!
In case of handicaps, it does not matter whether the person can actually say "Piet" or push a button named Piet, but by e.g. consequently blinking the left eye, or lifting the right finger, indicates that the person on the slide is, at least during the task, connected with the researcher Piet slide.