Scarface

Even whilst he is unconscious of his Messiahship, while he is still living in the Matrix (before the birth of consciousness when he wakes up in his pod naked with all the life support tubes connected), he already uses this name. The name 'Neil' is who is to be. It foreshadows his role as the champion of mankind.
             Morpheus.
             Morpheus in Greco-Roman mythology was the god of dreams, son of Hypnos (god of sleep).
             In the film Morpheus uses the phenomenon of dreams to explain to Neil the nature of the Matrix. That he is black is apt for sleep and dreaming are normally nighttime activities. It is in a netherworld apart from the light of day. That he is the oldest among the protagonists symbolizes sagacity and lends force and credence to his words.
             Zion.
             This Jewish name is very old, rich and has a number of meanings:.
             a hill in Jerusalem where the Temple was located .
             home of the Jews .
             haven of Judaism .
             the Jewish people .
             scene of Yahweh's messianic salvation .
             In the film the Agents are indefatigable in trying to find the whereabouts of Zion, for destroying it would mean the end of their troubles. But Zion is the hope of humanity, to lose it to the Agents would mean defeat. Historically till the present there has been a Jewish proclivity to hang on to the nation, the culture, the land. Jews have always had enemies and Zion has always given them a hope and a goal to continue striving and fighting for. Without the myth/symbol of Zion the Jews (or any people for that matter) would have long relented and succumbed.
             Nebuchadnezzar.
             He was Babylon king who conquered Jerusalem c. 600 BCE.
             I have not made a clear connection why the writers chose to name Morpheus' ship as so. Seems antithetical. For Jews Babylon represents the enemy, the destroyers of their home. Hence, why name a ship that represents the hope of Zion after one's vanquisher? Perhaps Nebuchadnezzar is a metonym for exile, for while the Matrix and the machines are in control of the world, our protagonists will remain as exiles in their own planet just as the Jews were in the time of Nebuchadnezzar.