Rabbi Dr. Raymond Apple has shared with The Jewish World his answer to this question. Apple served for 32 years as the chief minister of the Great Synagogue, Sydney, Australia’s oldest congregation. He is now retired and lives in Jerusalem. Apple blogs at http://www.oztorah.com.
The answer: The name does not come from the Talmud or Midrash. It derives from the Apocrypha, where it describes Judah, one of the Hasmonean brothers (II Maccabees 2:4).
Jewish tradition saw it as the initials of the battle-cry, “Mi Chamocha Ba-elim HaShem,” “Who is like You among the mighty, O Lord?” (Exodus. 15:11).
Other views link the name with a root that means “to extinguish”, since the Maccabees extinguished the Greek persecution, or with “makkav,” “a hammer”; Judah, like Charles Martel, was the hammer of his enemies.
The scholar and poet Aaron Kaminka (1866-1950) thought the name to be a corruption of “Machbanai,” a leading commando in the army of King David (I Chronicles 12:13).
David had 12 commandos from the tribe of Gad, who “separated themselves to David to the stronghold in the wilderness, mighty men of valour, men trained for war, that could handle shield and spear; whose faces were like the faces of lions, and they were as swift as the roes upon the mountains” (I Chronicles 12:8).
David has always been a role model for Jews, and it may be that Judah’s father, Mattathias, saw in his son the embodiment of an ancient Davidic hero.