From Black Squadron
His name comes from “Black Squadron,” the name of a special squadron appointed by General Organa to locate Lor San Tekka, as described in the comic of the same name:
He was the leader of this squadron (having been given authority by General Leia Organa to pick his team):
He was thus “Black Leader,” much as other members were, say, “Black Two”:
Note that this is not the same as the Black Squadron from Legends, which was commanded by Vader, and most certainly not affiliated with the Resistance or Leia Organa.
As to why the squadron was named “Black Squadron,” I’m not sure. Perhaps it was after the color of Poe’s ship (which, as can be seen in the pictures above, is black and orange), or the covert nature of their mission, or perhaps that was simply one of the colors that was available.