Carriage is the entire train car, not just the interior, so that's not the right word. Compartment and cabin would both work. The difference between the two words is that a cabin is meant for people, while a compartment could be for people, or for other things like baggage.

A train compartment is most commonly referred to as a "compartment" or a "coupe" (specifically in French and some international contexts). In a "compartment coach," the interior of the rail car is divided into several small, enclosed rooms accessible from a narrow side corridor. Each compartment typically features two rows of seating facing each other. If the compartment is designed for overnight travel, it is often called a "sleeper" or "berth." In North American rail terminology, these private rooms are frequently called "roomettes" or "bedrooms," depending on their size and amenities. While modern trains often utilize an "open saloon" or "coach" layout with a central aisle and open seating, the classic compartment remains a staple of luxury and long-distance travel, providing passengers with privacy and a quieter environment.