What are unique job titles in academia called?
In the United States, these types of "one-off" titles are typically given as a stage of promotion beyond full professorship.  The typical generic name would be "chaired professor," "distinguished professor," or "titled professor."  This is a rank that many faculty never reach, and typically the highest rank that a professor can achieve in the university as a professor---any further "promotion" is actually a change of position into management, e.g., dean, provost, president.

Such positions often come with a set of funds dedicated to support them, giving the faculty promoted to the position additional freedom of operation.  Often the exact title is set by the person or organization that endows support for the position.  For example, my thesis advisor is the "Panasonic Professor of Electrical Engineering" at MIT, meaning that his particular "one-off" position was endowed by the Panasonic corporation.  Such ties, however, typically mean little besides the name.