What does Daniel 1:6 mean?

Only four of the children taken into Nebuchadnezzar's reeducation program (Daniel 1:3–5) are mentioned by name. There would have been others, but these are the only ones who factor directly into Daniel's story. These were descendants of Jewish royalty taken, in part, so they could be molded into mediators between Israel and their Babylonian captors. These four boys are identified as members of the tribe of Judah, the same tribe as David and the Messiah, Jesus Christ (1 Samuel 17:12; Luke 3:23–38; Revelation 5:5; 22:16). Each carries a birth name referring to the God of Israel, but their new masters will assign them names tied to Babylonian religion:

Daniye'l, or "Daniel," means "God is my judge." His given Babylonian name will be Beltasha'tstsar, or "Belteshazzar," a call for protection from the false god Bel, or possibly "Lord of the straightened's treasure."

Chananyah, or "Hananiah," means "Yahweh has favored." His assigned pagan name will be Sadrak', or "Shadrach," possibly a reference to the false god Marduk, or as meaning "decree of the moon-god" or "I fear a god."

Miysha'el, or "Mishael," means "who is what God is?" This is similar to the name Miyka'el, or "Michael," which means "who is like God?" His new designation will be Meyshak, or "Meshach," meaning "guest of a king," or perhaps "I am humble before a god."

'Azaryah, or "Azariah," means "Yahweh has helped." He will be given the Babylonian name 'Abed Nagow, or "Abed-nego," meaning "servant of Nebo," in reference to the son of the Babylonian deity Marduk.

All four captives will demonstrate that names, themselves, do not define a person's destiny. Daniel will be renowned for his faithfulness to God (Ezekiel 14:14, 20; Daniel 6), only using the new Babylonian name is his book when others apply it to him. The other captives, most famously known be their new names of Shadrach, Meshach, and Abednego, will feature in a classic story about bravery in the face of persecution (Daniel 3).