I thought I would do a little research on the names of characters because Dr. P mentioned that many of them have significance.

Morpheus: is the Greek god of dreams. Morpheus has the ability to take any human's form and appear in dreams

Neo: Neo is a prefix signaling a "new" form or a revival of an old one.

Trinity: the Christian concept of God as three persons.

Some of the other crew members have names that make sense too, Mouse is small and mousy, Cipher deciphers the code of matrix.

I believe this is the name of their ship- Nebuchadnezzar. He was the king of Babylonia about 1100 BC. He was the king at the time when Israel was conquered and occupied by Babylonia, about the time of the Book of Daniel.

I'm not quite sure what the connection would be there.