Although the Order of St. Michael was NOT named after the Archangel Michael below is some information about the Angel. To note, the Order of St Michael was named after a friend of the Archbishop. However, the Archangel Michael is regarded as the patron angel of Warriors and, thus, is appropriate for this Holy Order.
Michael is the archangel mentioned in the Book of Revelation 12:7; in the Old Testament Michael is mentioned by name in the Persian context of the post-Exilic Book of Daniel. There Michael appears as "one of the chief princes" (10:13) who in Daniel's vision comes to the angel Gabriel's aid in his contest with the angel of Persia, and is also described there as the advocate of Israel and "great prince who stands up for the children of your (Daniel's) people" (10:21, 12:1).
The Talmud tradition rendered his name as meaning "who is like El (God)? (but literally "El's Likeness")" (compare the late prophet Micah), but according to Rabbi Simeon ben Lakish (AD 230–270), all the specific names for the angels were brought back by the Jews from Babylon, and many modern commentators would agree. Michael is one of the principal angels in Abrahamic tradition; his name was said to have been the war-cry of the angels in the battle fought in heaven against Satan and his followers.
He is so major an angel in Jewish lore that he was honored as the patron angel of the nations (out of seventy, or seventy-two according to other sources) who did not fall from grace, his bias entirely understood since it favored God's Chosen People..
Much of the late Midrash detail about Michael was transmitted to Christian mythology through the Book of Enoch whence it was taken up and further elaborated. In late medieval Christianity, Michael together with St George became the patron of chivalry, and the patron of the first chivalric order of France, the Order of Saint Michael of 1469. In the British honours system, a chivalric order founded in 1818 is also named for these two saints, the Order of St Michael and St George. St Michael is also considered in many Christian circles as the patron saint of the warrior. Police officers and soldiers, particularly paratroopers, regard him as their patron saint.
In the Book of Daniel The prophet Daniel experiences a vision after having undergone a period of fasting. In the vision, an angel identifies Michael as the protector of Israel (10:13, 21). Later in the vision (12:1), Daniel is informed that Michael will stand for Israel during the tribulation to come. There is no further mention of Michael in the Hebrew Bible.
In the Book of Joshua the numinous "captain of the host of the Lord" encountered by Joshua in the early days of his campaigns in the Promised Land (Joshua 5:13-15) has the character of Michael the Archangel, as the unnamed heavenly messenger is of supernatural and holy origin, likely sent by God:
Once when Joshua was near Jericho, he looked up and saw a man standing before him with a drawn sword in his hand. Joshua went to him and said to him, 'Are you one of us, or one of our adversaries?' He replied, 'Neither; but as commander of the army of the LORD I have now come.' And Joshua fell on his face to the earth and worshipped, and he said to him, 'What do you command your servant, my lord?' The commander of the army of the LORD said to Joshua, 'Remove the sandals from your feet, for the place where you stand is holy.' And Joshua did so. (Joshua 5:13–15, NRSV)
In the Book of Enoch, Michael is designated in the Book of Enoch, as "the prince of Israel" and the "archistratege" of God. He is the angel of forbearance and mercy (Enoch, xl:3) who taught Enoch the mysteries of clemency and justice (lxxi:2). In the book of Jubilees (i:27 and ii:1), the angel who is said to have instructed Moses on Mount Sinai and to have delivered to him the tables of the Law is most probably Michael.
In angeology, associates Michael with the color Red, the direction South and the element Fire. However, the Kabbalistic work, the Bahir (Sefer Ha-Bahir, Hebrew, "Book of the Brightness"), states that Michael is in fact attributed to the element Water
In other forms of angeology, Michael is said to be the spirit of the planet Mercury. He is ruler over Sunday and Thursday. He is the alchemy of motivation, activation and achievement. He is said to be bringer of the gift of patience, and angel of careers, courage, achievements, ambitions, motivation, and life tasks. Michael's candle colors are orange, white and gold. His color energies are orange, violet, white, crystal, gold, and brown.
In The Urantia Book, Jesus and Michael are identified with each other much as they are in the Jehovah's Witnesses. There have been a number of New Age gurus who have 'channelled' messages from Archangel Michael. Most notable among these are Elizabeth Clare Prophet--now no longer channeling due to Alzheimer's Disease--and Ronna Herman.