The neck i nreality would have to contain docking connections to attch it to teh saucer hull. It would also have power and water tarnsfer conduits. Elevator shafts, a few viewing ports, lounges, etc. Deflector Shield grids,anti accleration forcefield emitters,interual dampeners, equipment to polarize the hull would also be included. There would also be storage areas for spacesuits, and food , supplies ,tricorder,hand phasers, communicators and a life support euipment for heat and air, etc.
Some of these would be in use constantly. Other functions and stored suplies would come into use in case of the dorsal and engine hulls having to support the ship's population in case of a disaster involving loss of the saucer hull. Spare duty uniforms,work jumpsuits,sleeping cots and foodstuyffs would be there too in case of an emergency. There would be at least one dining area with windows on each side of the room so you would be able to look from one side of the ship to the other.