The indigenous Taino seem to have called it Ayiti. [fact]
The indigenous Taino seem to have called it Ayiti, but Columbus gave it a new name: La Española. On the northwest coast of the island, Columbus left behind a small group of sailors in the care of a local Taino chief. He returned the following year to find the settlement abandoned and destroyed, with most of those he had left behind buried nearby. The chief he had entrusted with his men claimed that a group of Caribs from another island had attacked and he had been powerless to defend the Spaniards. It is more likely that (not for the last time) the initial peace between Europeans and the indigenous peoples had devolved into violence.
Dubois, Laurent, Avengers of the New World_ …, loc. 40