Kind of like Dominica and Dominican Republic!!
Well, they are both Dominicans.
The Dominica Dominicans should change the name of their nationality. The Spanish Dominicans have been known as Dominicans at least since the 18th century, as that is when Dominicans was used -at least in writing- for the first time to refer to the natives of Spanish Santo Domingo (the natives from the French part were always known as French; the natives of the Spanish side were known interchangeably as Spaniards and Dominicans, those that were of color were referred to simply as mulatto Spaniards and black Spaniards in addition to Dominicans too; at least in colonial documents from the Spanish side they often refer to the natives of color from the French sidd as mulatto French and black French, but I'm not sure they themselves considered themselves French). The Dominica Dominicans call themselves that since they became independent from Britain in the 1960's even though their island has been called Dominica since Christopher Columbus gave the island that name.
And yes, I know that despite identical spelling they are not pronounced the same, but it's still an issue. They should be like Netherlands, because they are not Netherlanders but rather Dutch.
Anyway...