If the food is native to the caribbean and indicative of people or geographical features of the caribbean, then it may be a geographical indicator. For example, coffee and chocolate in Jamaica have been afforded geographical indicator protection. Certain agricultural may also fall under this category.
Geographic-related terms can be registered in many cases. The mark will be classified as descriptive, however, if the geographic area is known for the product. Think, for example, about Idaho potatoes, Florida oranges or Washington State apples.
A mark cannot be deceptively misdescriptive. For example, since consumers know Florida is known for oranges, a business growing oranges in Michigan cannot protect the mark “Florida oranges.” Consumers would be misled into thinking that the oranges originated in Florida. Similarly, a U.S. company cannot protect a primarily geographic mark in “Columbian coffee.” Consumers would mistakenly make the association to Columbia as the source of the coffee product.
However, a mark may not be “primarily geographically descriptive” if there are several different locations for the product, the name is also a surname or the name doesn’t import information about product origin. It may be the case that marks with terms such as Hollywood, New York, Miami Beach, Paris and other famous places are used in marketing but have no relation to the product’s origin. Popular examples include “Hollywood Burgers” (one would not assume that the burgers are made in Hollywood) and “Jilbere de Paris” clothing line.
In addition to the other comments, I would add that it would be important to conduct a search to make sure there are no existing trademarks, including certification marks, that would bar your application. Importantly, note that there is a certification mark at the USPTO for PURE CARRIBEAN for goods.
An example of a geographic indicator which became generic is "FETA" for cheese and "parmesan" for hard cheese. An example of a USPTO certification mark is "IDAHO" owned by the State of Idaho Potato Commission, "100% Napa Valley" owned by Napa Valley Vintners Association for grape wine, or "Tequila." Certification marks differ from other trademarks as the owners cannot use the mark on products and must test the products against certain "criteria" standards. You should consult with a trademark attorney before filing your application.