Daniel 1: 8 But Daniel determined in his heart that he would not defile himself with the king’s royal food, nor with the wine which he drank: therefore he requested of the prince of the eunuchs that he might not defile himself. 9Now God gave Daniel favor and compassion in the sight of the prince of the eunuchs. 10 The prince of the eunuchs said to Daniel, “I fear my lord the king, who has appointed your food and your drink: for why should he see your faces worse looking than the youths who are of your own age? So would you endanger my head with the king.” 11 Then said Daniel to the steward whom the prince of the eunuchs had appointed over Daniel, Hananiah, Mishael, and Azariah: 12 “Test your servants for ten days; and let them give us vegetables to eat, and water to drink. 13 Then let our faces be looked on before you, and the face of the youths who eat of the king’s royal food; and as you see, deal with your servants.” 14 So he listened to them in this matter, and tested them ten days. 15 At the end of ten days their faces appeared better and fatter than all the youths who ate of the king’s royal food. 16 So the steward took away their royal food, and the wine that they should drink, and gave them vegetables. NET
Daniel and friends were in the first group taken to Babylon. A second group is taken a bit later followed by the destruction of the Temple about seven years later.
In these verses, we see the program that Nebuchadnezzar is planning for these young men. The first step is education (or really re-education) as they must be immersed in Babylonian culture. Next is food and drink as the king is going to take care of them during their studies. Third is to give them new names to demonstrate to all just who these young men serve. Finally, they will enter government service.
None of the four put up any resistance to all that is happening to them but suddenly draw the line at eating Babylonian food. Many assume Daniel is doing this because of the dietary laws. Among other things, these laws forbid certain animals to be eaten, lay out the precise means for butchering and preparing those animals that may be eaten and forbid grape products produced by non-Jews. (See: https://www.jewishvirtuallibrary.org/overview-of-jewish-dietary-laws-and-regulations). Others will say it was his fear that this food and drink was connected with idolatry and the worship of Babylonian gods leading to personal defilement. It could even be a little of both.
“It was the custom to throw a small part of the viands and wine upon the earth, as an initiatory offering to the gods, so as to consecrate to them the whole entertainment (compare Deut 32:38). To have partaken of such a feast would have been to sanction idolatry, and was forbidden even after the legal distinction of clean and unclean meats was done away (1Corinthians 8:7, 10; 10:27 and 28)” Jamieson-Fausset-Brown Bible Commentary https://biblehub.com/commentaries/jfb/daniel/1.htm
Problems arise for the faithful when interacting with a culture for whom faith is a foreign concept. This is true for Daniel as a Jew and for us as Christians. For example, in Acts 5 Peter and the other apostles are instructed by the San Hedrin not to teach anything in this name. Their response is that they will keep preaching no matter what the council may say. Like the apostles, the question for Daniel and his group is to focus on who they owe their loyalty to. By eating vegetables they still serve Babylon but keep allegiance to God.
The key thing to see here is that Daniel and his companions are staying true to their faith in a foreign land that was doing everything it could to yank them away from it. With that said, some see a contradiction in Daniel 10 as it indicates that he has eaten meat and drunk wine but the difference is that by this point, Daniel is in control of what he eats and drinks and the preparation thereof.
In our dealings with the culture around us there are three approaches that are typically followed. The first is to obey both God and the laws of government under the idea that the governing authorities are appointed by God (Romans 13:1-7). Our witness to the world will be one being both good citizens and good Christians. The second approach is separation where we withdraw in order to protect ourselves against the impact the surrounding culture could inflict on us. In this view Caesar is one thing and Christ is another and neither shall ever intersect. Here, our testimony to the world is to be a light on a hill that other people can see. (The Amish and some forms of monasticism are examples of this). The third way is a transformational approach where we will engage and work within the culture.
For the Christians are distinguished from other men neither by country, nor language, nor the customs which they observe. For they neither inhabit cities of their own, nor employ a peculiar form of speech, nor lead a life which is marked out by any singularity. The course of conduct which they follow has not been devised by any speculation or deliberation of inquisitive men; nor do they, like some, proclaim themselves the advocates of any merely human doctrines…..They dwell in their own countries, but simply as sojourners. As citizens, they share in all things with others, and yet endure all things as if foreigners. Epistle to Diognetus
As to the name change, notice that all four of the young men’s Jewish names either end in “el” (referring to Elohim) or “ah”(referring to Yahweh). In Hebrew, Daniel’s name means “God is my judge”, Hananiah means “God has been gracious to me, Mishael means “the powerful one of God” and Azariah means “the help of Jehovah”. It is generally thought in a similar fashion that their new names refer to gods of the Babylonians, For example, Daniel’s new name is tied to “Bel” a god of Babylon.
Depending upon the translation, the people teaching Daniel and his companions are typically described as either “eunuchs” or “court officials”. The linguistic problem is that the Hebrew word being translated here (saris) can refer to someone who is a eunuch or simply to a court official or minister. In Genesis, this term is used to describe Potiphar who happens to be married. Some will argue that the four can’t have been castrated or they could no longer be described as physically perfect while others think that because their overseer is a eunuch that they were also made eunuchs.
Daniel 1:17 To these four young men God gave knowledge and understanding in every kind of literature and wisdom. And Daniel had insight into all kinds of visions and dreams. 18 Now at the end of the time specified by the king, the chief official presented them to Nebuchadnezzar. 19 And the king spoke with them, and among all the young men he found no one equal to Daniel, Hananiah, Mishael, and Azariah. So they entered the king’s service. 20 In every matter of wisdom and understanding about which the king consulted them, he found them ten times better than all the magicians and enchanters in his entire kingdom. 21 And Daniel remained there until the first year of King Cyrus. BSB
The point being made in verse 21 is not that Daniel lived until the first year of King Cyrus (we will see in chapter 10 that he lived at least two more years) but rather that he was there throughout the entire 70 year exile that ended with Cyrus.