"Among these were some from Judah: Daniel, Hananiah, Mishael and Azariah." NIV translation
Among the men taken to be trained were four in particular: Daniel whose name means "God is my judge", Mishael "Who is what God is", Hananiah "Whom Jehovah has graciously given" and Azariah "whom Jehovah helps". All of these names give us the expectation of God about to do a mighty work.
"The chief official gave them new names: to Daniel, the name Belteshazzar; to Hananiah, Shadrach; to Mishael, Meshach; and to Azariah, Abednego." NIV translation
The first step in making these young men proper servants of Babylon was to make them forget their old identity. Therefore, they were given new names and each of them had a meaning: Belteshazzar "Bel's prince" Bel was the principal god of Babylon and it would have been an attempt to flatter Daniel by calling him a prince of their god.
Meshach "little sheep" who was one they thought they could lead astray with this idolatry. Shadrach "rejoicing in the way" was an attempt to get them to see how they would prosper by turning their backs on the one true God. Abednego "servant of Nebo" really lets us see the purpose and that was to get them to join in idolatry. This is a good lesson for us today, in that, we must continually remind ourselves that our identity is in Christ or we can be enticed to forget.
"But Daniel resolved not to defile himself with royal food and wine, and he asked the chief official for permission not to defile himself this way." NIV translation
We see, here, that Daniel had a choice of whether to take the easy way or to listen to God. He chose to listen to God but we also see that he was not arrogant about it. Instead of flatly refusing to eat the king's food, he asked for permission from the chief official. That is a good example for us as well in that how we go about something can be just as important as what we are doing. Daniel honored God not only through obedience but also through his humility.
"Now God had caused the official to show favor and sympathy to Daniel, but the official told Daniel, 'I am afraid of my lord the king, who has assigned your food and drink. Why should he see you looking worse than the other young men your age? The king would then have my head because of you.'" NIV translation
The official was in a tough position as God had caused him to actually like Daniel and to want to help him but, now, this could put his life in danger. He did not understand that God was with them and going to ensure that they were healthy. If they were not and the king noticed, he would know that he had been disobeyed. The penalty for disobeying the king would have been death.