What is the name of he island where both countries of haiti and the dominican republic are found?

In Haiti, they call it: "L'ile d'Haiti" means "Haiti Island". The reason of this name is probably because at the beginning the name of the whole Island was Haiti, Quisqueya or Boyo. Another name of the Island was Hispaniola "Little Spain" to show its affiliation or its likeness in ressources to Spain.