What is the name of the Cajun rice dish made with chicken livers?

The Cajun rice dish made with chicken livers is called dirty rice.

Dirty rice is made from white rice cooked with finely chopped organ meat, traditionally chicken livers and often giblets. The meat gives the rice its characteristic darker, “dirty” appearance. Bell pepper, celery, and onion—the Louisiana cooking combination often called the “holy trinity”—are common additions, along with cayenne and black pepper.

The dish developed from resourceful Southern cooking, in which inexpensive rice and less-prized cuts of meat were combined into a filling meal. It became associated with both Louisiana Creole and Cajun foodways and later spread throughout the American South.

Dirty rice is sometimes called Cajun rice or rice dressing, but those names can describe variations made with ground beef, pork, or sausage instead of chicken liver. That overlap explains the wrong-option appeal, while jambalaya is a different rice dish with its own preparation and ingredient traditions.