From Dragon Quest Wiki
A Dream Scenario is an event that the young Hero undergoes before beginning his/her journey in Dragon Quest III: The Seeds of Salvation.
Absent from the Nintendo Entertainment System version of the game, these events are present in all of the remakes from the Super Famicom to the Nintendo Switch remakes of Dragon Quest III.
The Hero (or rather the player) is asked by a voice to give his/her real name, plus month and day of birth.
Afterwards The Hero is asked a series of random questions with which the dream given is dependant on the answer given to some.
The voice determines the Hero's default personality by how he/she handles the dream.
After which states that the Hero will soon awake and that they will meet again someday.