To get the ball rolling, here is a glossary of some of the matrix names, clipped and pasted.
Matrix Glossary
Birth: When he is "unplugged" from the Matrix, Neo resembles a newborn. Once his "umbilical cords" are removed, we see that he is hairless, confused, and covered in a type of amniotic fluid. He falls down a long tube and into a pool of water. After this presumed baptism, he is carried up, with his limp body making a cross silhouette. Neo had to be "born again" before he could begin his mission.
Buddhism: The chief problem faced by humanity, according to Buddhist thought, is not sin or evil: it's ignorance of the true reality. The lack of an explicit divine being and references to "focus," "path," and "free your mind" also smack of Buddhist influence. Matrix rebels download truth and reprogram their minds to achieve salvation.
Cypher: The name of this traitor who excels at Matrix code means, according to Webster's Dictionary: Zero...a person or thing of no importance or identity...a system of secret writing based on a key. His character has many parallels to Judas. At one point he exclaims, "Whoa, Neo. You scared the bejeezus out of me."
Evil: Agent Smith tells Morpheus that the original Matrix world was "designed to be a perfect human world." No one accepted the program, he explains, because "human beings define their reality through misery and suffering." By drawing on parts of Genesis and comparing humans to a virus, Smith establishes evil as a natural, intrinsic state of human nature.
God: God does make a cameo in The Matrix only as an expletive from Trinity. Yet the word "miracle" is used in clear cases to signify the need - and reality - of divine intervention. But there's no implied sense of a covenant between God and man.
Jesus Christ: The name Jesus is often used in association with Neo, most explicitly when Choi, a drug user, thanks Neo for providing him with illicit software. "Hallelujah. You're my savior, man. My own personal Jesus Christ."
Matrix: Literally, a computer program used to imprison mankind. According to Webster's, "matrix" means: 1) orig., the womb; uterus 2) that within which, or within and from which, something originates, takes form, or develops. At its heart, The Matrix is a story about birth and creation.
Morpheus: Neo's mentor. Some observers identity him with John the Baptist, since both men were appointed to prepare the way for a messiah. In Greek mythology, Morpheus, the son of Hypnos, was the god of dreams.
Music: The final song, played by Rage Against The Machine, is "Wake Up."
Neo: The messiah. This is Thomas Anderson's virtual name. Literally meaning "new," Neo is also referred to as the "One," which is an anagram for Neo.
Nebuchadnezzar: Morpheus's ship. This figure referenced in the Book of Daniel was the powerful king of ancient Babylon who suffered from troubling dreams. The name literally means "Nebo, protect the crown."
Numerology: Neo's apartment number is 101, suggesting that he's "the one." Neo is shot in apartment number 303, and after 72 seconds (72 hours = 3 days), he rises again.
Phone calls: In keeping with prophetic tradition, Neo is "called" to his task, not by a burning bush, but a FedEx employee. Their brief exchange - "Thomas Anderson?" | "Yeah, that's me." - mirrors Bible language constructions used to signify special identity.
Postmodernism: Neo hides his illicit software within a chapter titled "On Nihilism" within a volume called "Simulacra and Simulation," by Jean Baudrillard. This seminal work of postmodernism advances the idea of a copy without an original. The Wachowski brothers assigned Keanu Reeves to read this book before filming began.
Thomas Anderson: The Apostle Thomas was also called Didymus, which in Greek means "twin" or "double." Anderson means "son of man," one of the titles Jesus uses for himself. The twin names suggest his dual nature. As "Mr. Anderson," he is vulnerable to the powers of the evil agents. As "Neo," he has dominion over them.
Trinity: Her kiss restores Neo from death. The doctrine of the three modes of God is central to Christian orthodoxy, yet the word "trinity" never actually appears in the Bible. Neo deepens the mystery of who Trinity is when he says to her, "I just thought, um...you were a guy."
Logos: The altered studio logo at the opening of the film may be highly significant. The Matrix-coded WB letters could simply be the Wachowski brothers thumbing their nose at the Warner Bros. But by altering the logo - from the Greek term "logos," for word - the film's opening does two things. First, it corrupts the Gospel of John, which begins with "In the beginning was the Word...". Second, it asserts that metaphysical meaning can be gleaned by mining deep into words, or code.
Zion: The last human city. In the Old Testament, Zion refers to the royal capital of David. Matrix agents desire the codes to Zion above all else.