Their Babylonian enemies, by whom they were enslaved, changed their names. The meanings of their true names declared who God said they were. Their new Babylonian names tried to take that identity away from them:
"God has favored" --> "royal" or "the great scribe" (Hananiah --> Shadrach)
"who is what God is" --> "guest of the king" (Mishael --> Meshach)
"Jehovah has helped" --> "servant of Nebo [a Babylonian god]" (Azariah --> Abednego)