Meaning of Names in the Trilogy:

Matrix

* Biology: A basic substance without inner structure
* Mathematics: A rectangular scheme of numbers
* Latin: Source; cause; mother animal; uterus

Thomas A. Anderson

* Ander = "Man" (from the Greek 'Andro')
So Neo is the Son of Man. Son of Man is what Jews refer to as the Messiah, while Son of God is what Christians refer to as Jesus. Moreover "Neo Anderson" would mean the "New Son of Man".
* "Thomas A." is probably related to "Thomas Aquinas" - a saint of the Catholic church that wrote Summa Theologica. Check out more on wikipedia: http://en2.wikipedia.org/wiki/Thomas_Aquinas

Trinity

* Trinity, referring to the Christian idea of the divine

* Check out more on wikipedia: http://en2.wikipedia.org/wiki/Trinity

Morpheus

* The Wachowski brothers, writers and directors of The Matrix films were fans of Neil Gaiman and based the character of Morpheus on the title character from The Sandman, also adopting one of his most common pseudonyms, Morpheus. They gave Fishburne some or all of the Sandman series to read, and the style of speech and mannerism of the Matrix character are heavily informed by the Sandman character, although since The Sandman is only a graphic novel, much of the tone and inflection is an original (though recognizable) interpretative creation on Fishburne's part. This connection is hinted at again in Enter the Matrix when Niobe calls Daniels Institute of dreams to get in touch with Morpheus.

* Morpheus is the Greek god of dreams
Morpheus: "Have you ever had a dream, Neo, that you were so sure was real. What if you were unable to wake from that dream. How would you know the difference between the dream world and the real world?"
Morpheus: "You've been living in a dream world, Neo."
Morpheus: "The Matrix is a computer generated dream world"
Morpheus: "Good night, Zion. Sweet dreams."
Morpheus: "I have dreamed a dream, and now that dream has gone from me."

Nebuchadnezzar

* Nebuchadnezzar is a king mentioned in the bible who is haunted by bad dreams
* Nebuchadnezzar is Morpheus' ship

Zion

* "Zion" in the sense of "Jerusalem"

* Lambert Wilson (who plays the Merovingian) mentions in an interview that Zion is related to the "Priory of Zion" (Prieure du Notre Dame du Sion), a secret society, with connections to Knights Templar, Roscicrucianism, and Freemasonry.
From crystalinks.com/templars5.html:
"The real mission of the Templars and Priory of Zion: To safeguard not just the treasure of the Crusades, but to preserve the Grail... The Merovingians were considered in their day to be quasi-mystical warrior-kings vested with supernatural powers."
Zion originally was the specific name given to a Jebusite fortress near modern-day Jerusalem that was conquered by David. The original fortress was located on the hill in southeastern Jerusalem.

* Zion, or Sion, is an archaic term that originally referred to a section of Jerusalem, which, by Biblical definition, is the City of David. After the death of King David, the term Zion came to refer to the hill in Jerusalem which was the site of Solomon's temple. Later, Zion came to refer to temple and the temple grounds themselves. Beyond that, Zion is used to symbolize Jerusalem and the Promised Land of God to come, in which God dwells among his chosen people.

Modern use
The longing for Zion of the Babylonian Hebrews was adopted as a metaphor by Christianized Black slaves. Thus, Zion symbolizes a longing, by wandering peoples, for a safe homeland. This could be a literal place such as in Africa for Rastafarians for example. For others, it has taken on a more spiritual meaning —a safe spiritual homeland, like in heaven, or a kind or peace of mind in one's present life.

Zion is a city that Mormons believe will be built in Jackson County Missouri, and a common reference to both North and South America. In a spiritual sense, Zion is regarded by Mormons as an utopian society of "pure in heart" believers where all citizens have all things in common. 

Cypher

* "Cypher" sounds similar to "Lucifer"
* "Cypher" is another word for "void" / "zero" / "nil" / "not real" / "not entity"
* A cipher is a code

Niobe

* A mortal woman in Greek mythology, Niobe, daughter of Tantalus and either Euryanassa, Eurythemista, Clytia, Dione, Laodice, wife of Amphion, boasted of her superiority to Leto because she had fourteen children (Niobids), seven male and seven female, while Leto had only two. Apollo killed her sons as they practiced athletics, with the last begging for his life, and Artemis her daughters. Apollo and Artemis used poisoned arrows to kill them, though according to some versions a number of the Niobids were spared (Chloris, usually). Amphion, at the sight of his dead sons, either killed himself or was killed by Apollo after swearing revenge. A devastated Niobe fled to Mt. Siplyon in Asia Minor and turned into stone as she wept, or committed suicide. Her tears formed the river Achelous. Zeus had turned all the people of Thebes to stone and so no one buried the Niobids until the ninth day after their death, when the gods themselves entombed them.

Mt. Sipylus has a carving of a female face on it that the locals claimed was Niobe, though it was probably originally intended to be Cybele. The rock appears to weep because it is porous limestone and rainwater seeps through the pores.

Aedon was the queen of Thebes who attempted to kill the son of her rival, Niobe, also her sister-in-law (Aedon was married to Zethus), and accidentally killed her own daughter, Itylus instead and thus, the gods again changed her into a nightingale. 

Apoc

* "Apoc" = Apocalypse

Merovingian

* The Merovingians were a dynasty of Frankish kings who ruled a (frequently fluctuating) area in parts of present-day France and Germany from the 5th to 8th century AD. They were sometimes referred to as the "long-haired kings" by contemporaries, though the significance of their long hair is not clear.

The Merovingian dynasty (see List of Frankish Kings) owes its name to Merovech (sometimes Latinised as Meroveus or Merovius), leader of the Salian Franks from about 447 to 457, and emerges into wider history with the victories of Childeric I (reigned about 457-481) against the Visigoths, Saxons and Alamanni. Childeric's son Clovis I went on to unite most of Gaul north of the Loire (486), to adopt Roman Catholicism (496), and to decisively defeat the Visigothic kingdom of Toulouse in the Battle of Vouillé (507).

In the early 7th century, the Merovingian kings began to allot more and more day-to-day administration to a powerful official in their household called the maior domo. This Latin title literally translates to "big man in the house"; the usual English translation is Mayor of the Palace, although this official was not a mayor in the modern sense of the word. The office of Mayor of the Palace itself became hereditary in the Carolingian family. Soon the Mayors were the real military and political leaders of the Frankish kingdom, a fact that became manifest when, in 732, an invading Arab army from Spain was defeated by an army led not by the King, but by the Mayor Charles Martel. The contemporary Merovingian kings of this period are by comparison shadowy figures who did not travel beyond their palaces or have much influence over government.

Charles' son, the Mayor Pippin III, gathered support among Frankish nobles for a change in dynasty. When the Pope appealed to him for assistance against the Lombards, he insisted that the church sanction his coronation in exchange. So, in 751, Childeric III, the last Merovingian, was deposed. He was allowed to live, but his long hair was cut and he was sent to a monastery.

Merovingian coins are on display at Monnaie de Paris, (the French Mint) at 11, quai de Conti, Paris, France.

According, however, to certain esoteric versions of history (the Knights Templar, in particular), the Merovingian kings were direct descendants of Mary Magdalene and Jesus Christ once they arrived in southern France following Christ's crucifixion and "resurrection." Some say that the Roman church killed off all remnants of this dynasty (i.e., both the "Cathar Heresy" of Languedoc early on and Templars - also purportedly descendants of Christ - during the Inquisition) in order to gain power through the "spiritual" dynasty of Peter instead of the "holy blood" (i.e. Sangreal) of Mary Magdalene's descendants. 

Persephone

The daughter of Zeus and Demeter, Persephone ("she who destroys the light") (also Kore, "maiden;" Roman equivalent: Proserpina) became the goddess of the underworld when Hades abducted her from the Earth and brought her into the underworld.

She was innocently playing with some nymphs (or Leucippe) or Oceanids) in a field in Enna when he came; the nymphs were changed into the Sirens for not having interfered. Life came to a stand still as the depressed Demeter (goddess of the Earth) searched for her lost daughter; Helios, the sun, who sees everything, finally told her what had happened.

Finally, Zeus could not put up with the dying earth and forced Hades to return Persephone. But before she was released, Hades tricked her into eating six pomegranate seeds, which forced her to return six months each year. In some versions, Ascalaphus told on Persephone eating the pomegranate seeds. When Demeter and her daughter were together, the Earth flourished with vegetation. But for six months each year, when Persephone returned to the underworld, the earth once again became a barren realm. In alternate version, Hecate rescued Persephone. She is a life-death-rebirth deity.

Persephone, as Queen of Hades, only showed mercy once, because the music of Orpheus was so hauntingly sad. She allowed Orpheus to bring his wife, Eurydice, back to the land of the living as long as she walked behind him and he never tried to look at her face until they got to the surface. Orpheus agreed but failed and lost Eurydice forever.

Persephone also figures into the famous story of Adonis. Once Adonis was born, Aphrodite took him under her wing, seducing him with the help of Helene, her friend, and was entranced by his unearthly beauty. She gave him to Persephone to watch over, but Persephone was also amazed at his beauty and refused to give him back. The argument between the two goddess' was settled either by Zeus or Calliope, with Adonis spending four months with Aphrodite, four months with Persephone and four months of the years with whomever he chose. He always chose Aphrodite because Persephone was the cold, unfeeling goddess of the underworld.

When Hades pursued a nymph named Mintho, Persephone turned her into a mint plant.

Persephone was the object of Pirithous' affections. Pirithous and Theseus, his friend, pledged to marry daughters of Zeus. Theseus chose Helen and together they kidnapped her and decided to hold onto her until she was old enough to marry. Pirithous chose Persephone. They left Helen with Theseus' mother, Aethra and travelled to the underworld, domain of Persephone and her husband, Hades. Hades pretended to offer them hospitality and set a feast; as soon as the pair sat down, snakes coiled around their feet and held them there. 

Seraph

From the Hebrew "Seraphim". According to Christian angelology, the seraphim are the highest order of angels, serving as the caretakers of God's throne and continuously singing his praises. Prior to his fall from grace, Lucifer was counted among the seraphim, outshining all others. Seraphim are often depicted as 6 wings radiating from a center either concealing a body or without a body.

Architect

* Physicists often refer to God as the Architect 

* Freemasons call their head leader is the "Grand Architect" (I'm pretty sure)

Bane

* Bane is defined as "something that causes misery or death." It is often said in the phrase "bane of all humanity."