Who should design the nozzle of jet engines on aircraft?
I suspect there will be some collaboration between the two (as the nozzle partly determines the performance of the engine), but this is primarily the domain of the aircraft designer. Only he/she knows the (aerodynamic) specifics of the integration of the power plant on the aircraft and is able to make a proper trade-off, for example regarding ground clearance. 

A textbook example of that is the integration of the CFM56 on different aircraft. The Boeing 737 uses flattened nacelles, whereas the nacelles are circular  on the A320-family. The flattened ones are structurally less efficient, but at aircraft level, it was an easier/better option than increasing the landing gear height. (This problem, by the way, is still haunting the 737-series. A recent innovation featured on the 737 MAX-10 extends the landing gear using a new lever to prevent the tail from scraping the runway on rotation, another problem of a shorter landing gear.)