Which role manages vanities like hair, make-up, and wardrobe on set?

The role that manages vanities such as hair, make-up, and wardrobe on set is the Costume Designer. This position is specifically responsible for creating the characters' visual identities through their clothing and accessories, ensuring that the costumes support the story and character development.

The Costume Designer collaborates closely with the director and other design departments to ensure that all wardrobe choices align with the overall vision of the production. While roles like the First Assistant Director and Second Assistant Director focus on the logistical and scheduling aspects of film production, the Costume Designer is dedicated to the artistic element of clothing and appearance, which is essential for the visual storytelling in film.

The Production Designer oversees the overall visual look of the film, including sets and locations, but does not directly manage hair and make-up. Therefore, in the context of managing vanities on set, the correct choice is the Costume Designer.