Mathematically, black holes are described by solutions of the field equations of the theory of general relativity, the first of which was published in 1916 by Karl Schwarzschild. Another highly relevant solution, representing a rotating black hole, was found by Roy Kerr in 1963.
It was only around half a century after Schwarzschild's solution, however, that the term black hole was used to describe these objects. Who coined it? Conventional wisdom attributes the origin of the term to the prominent North American physicist John Wheeler who first used it in a general audience article published in 1968. This, however, is just one side of a story that begins two hundred years before in an Indian prison of the 18th century.
To celebrate in 2018 the 50 years of the name black hole, Carlos Herdeiro and José Sande Lemos wrote an article with title "The black hole fifty years after: Genesis of the name". The article is in Portuguese and has been now published in https://www.spf.pt/magazines/GFIS/392, Gazeta de Física 41(2), 2 (2018). For the English version of the paper see arXiv:1811.06587 [physics.hist-ph].