Carnival corporation ships like Carnival, Princess and Holland dock at Amber Cove
All other cruise lines like MSC, Norwegian, Virgin, Royal dock a few miles down the road at Taino Bay
What makes everything very very confusing is these unofficial ships in port websites like cruisemapper, cruisetimettables, etc, etc call this port Puerto Plata so you see all cruise line ships in port.
amber cove does has an official port website that only show the carnival ships in port: https://ambercove.com/