If a person from the Dominican Republic is called a Dominican, what is a person from the the Caribbean island state of Dominica called?

The indigenous people are called Caribs, while other people from Dominica are called Dominicans. It is spelled the same as it would be for someone from the Dominican Republic, but it is pronounced differently.

The indigenous people of the island, the Caribs, have a territory similar to the Indian reserves of North America. The official language is English in consequence of its history as a British colony, territory, and state, though a French creole is spoken by many, especially people of older generations. The demonym or adjective is "Dominican" in English, same as that for the Dominican Republic, but unlike the Dominican Republic, in which the stress is on the first "i", the stress is on the second "i".

https://en.wikipedia.org/wiki/Dominica#Demographics