If the Spanish were the first ones there and established colonies and settlements then the names and possibly the name of the island itself would come from Spanish/Latin roots. However, since the English and the French have the most dominant impact on the culture the Spanish names/words would be borrowed into English and follow the English pronunciations. After all, the name "America" came from Latin origins named after the Italian explorer "Amerigo". So you could use ideas like this to create a name and a history for your island nation.