This was the surname of American president Grover Cleveland (1837-1908). It is also the name of an American city, which was founded by surveyor Moses Cleaveland (1754-1806).
The FIRST: It is an obvious use of a descriptive term that crystallized from a nickname into an acceptable family name. Many such names as BLACKMORE, BLACK, BLAKEMAN, BLACMAN, AND BLACKMAN, testify to the darker tone of some of our forbearers countenances. The term has nothing to do with race or nationalistic characteristics, but possibly began as a nickname for a particular individual as "BLACK a' Moor" or black as a Moor. Stephen le Blac (to distinguish him from Stephen le Blane) is now Blake: the name "Nutbrown" was an early name, existing at least until 1630. Our Browns began in the same way.
The SECOND: Many names had their beginning because a person lived in a location easy to describe and thus distinguished the person from another of the same name living elsewhere. For example, Steven atte BLACKMOOR resided close to the murky and gloomy heath or moor.