I think it comes from the name the French colonists gave it - Dominique.
It gets confused with the larger Dominican Republic, which is the western half of the island that also contains Haiti (which I pronounce Ha-EEty, but which some (Americans?) tend to pronounce Heighty.
There can also be confusion between Granada (Graneyda) in the Caribbean and Granada (Granahda) in Spain; and in England between Gillingham in Dorset and Gillingham (Jillingham) in Kent.