The position of family history center director is a stake calling.
The assigned high councilor oversees all family history centers in the stake. He recommends members to be called as family history center directors and assistant directors (if needed). A member of the stake presidency or the high councilor calls and sets apart these members. (Leader’s Guide to Temple and Family History Work: To Turn the Hearts (2011), 24).
If there are multiple family history centers in your stake, each director should be called and set apart in accordance with these guidelines.