There is a person sometimes called "the black pope," but his existence is not a secret and he does not have anywhere near as much power as the real pope. "The black pope" is a nickname given to the Father General of the Society of Jesus. When the Jesuits were the most prestigious, influential missionary order in the world, the people of Rome began to speak jokingly of their head as a second pope. They called him "the black pope" because he wore the Jesuits' black clerical garb, in contrast to the real pope, who wore white and became known as "the white pope."
"The black pope" does not have authority over anyone but Jesuits. Sometimes people point to him as evidence of a conspiracy in the Vatican, but what they really have is a garbled understanding of a Catholic in-joke.