That's QT (2000)

When the game begins, the player wakes up and washes their face in their bathroom. Each time their face is washed, they can change their character's profile from six different expressions (eight in the DS version). During the following interview, the player can give their character a name and gender. If they answer the following quiz questions correctly, they will get a small prize.

Though there are short story segments separating the stages throughout the game, the majority of the gameplay is separated into three stages.