First, Haiti achieved independence in 1804, way before the US Civil-War. Haiti was originally called Saint-Domingue
Wikipedia says that name was originally "Ayiti" as derived from Taíno and African languages
At the end of the double battle for emancipation and independence, former slaves proclaimed the independence of Saint-Domingue on 1 January 1804, declaring the new nation be named "Ayiti", both a Native American and African term, meaning "home or mother of the earth" in the Taíno-Arawak Native American language and "sacred earth or homeland" in the Fon African language, to honor one of the indigenous Taíno names for the island.
Ayiti (land of high mountains) was the indigenous Taíno or Amerindian name for the island.
The book "A Brief History of the Caribbean" confirms this
Saint-Domingue finally belonged to the black majority after 15 years of devastation. On January 1, 1804, Dessalines and his generals proclaimed Haiti's independence, choosing an aboriginal word (meaning "the land of the mountains") to replace the French name Saint-Domingue.
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