Acadiana-style Cajun jambalaya is often called brown jambalaya around New Orleans.
The name refers to the dish’s appearance and regional identity. Acadiana-style jambalaya usually omits tomatoes, unlike New Orleans-style jambalaya. Cooks typically brown the meat first, then sauté the vegetables and add stock, seasonings, and rice. The browned bits stuck to the bottom of the pot, known in Louisiana cooking as sucs, help give the finished dish its brown color.
In Acadiana itself, people generally call this preparation simply jambalaya. The label “brown jambalaya” is especially useful in the Greater New Orleans area, where the term distinguishes the Cajun style from the local tomato-based version, often called red jambalaya in Acadiana.
The regional names can cause confusion because families and restaurants do not all follow identical recipes. Some cooks use different meats, seafood, or cooking methods, and the lower Westbank near New Orleans has families who use the Acadiana terminology. Still, brown is the standard color term for the traditional Cajun style in the question.