"Chapter 39—In the Court of Babylon This chapter is based on Daniel 1 . Among the children of Israel who were carried captive to Babylon at the beginning of the seventy years’ captivity were Christian patriots, men who were as true as steel to principle, who would not be corrupted by selfishness, but who would honor God at the loss of all things. In the land of their captivity these men were to carry out God's purpose by giving to heathen nations the blessings that come through a knowledge of Jehovah. They were to be His representatives. Never were they to compromise with idolaters; their faith and their name as worshipers of the living God they were to bear as a high honor. And this they did. In prosperity and adversity they honored God, and God honored them. PK 479"
"In the third year of the reign of Jehoiakim king of Judah came Nebuchadnezzar king of Babylon unto Jerusalem, and besieged it. And the Lord gave Jehoiakim king of Judah into his hand, with part of the vessels of the house of God: which he carried into the land of Shinar to the house of his god; and he brought the vessels into the treasure house of his god. And the king spake unto Ashpenaz the master of his eunuchs, that he should bring certain of the children of Israel, and of the king’s seed, and of the princes; Children in whom was no blemish, but well favoured, and skilful in all wisdom, and cunning in knowledge, and understanding science, and such as had ability in them to stand in the king’s palace, and whom they might teach the learning and the tongue of the Chaldeans. And the king appointed them a daily provision of the king’s meat, and of the wine which he drank: so nourishing them three years, that at the end thereof they might stand before the king. Now among these were of the children of Judah, Daniel, Hananiah, Mishael, and Azariah: Unto whom the prince of the eunuchs gave names: for he gave unto Daniel the name of Belteshazzar; and to Hananiah, of Shadrach; and to Mishael, of Meshach; and to Azariah, of Abed–nego."
The EGW passage explicitly states it is based on Daniel 1 and summarizes the events and principles found there.
"The fact that these men, worshipers of Jehovah, were captives in Babylon, and that the vessels of God's house had been placed in the Temple of the Babylonish gods, was boastfully cited by the victors as evidence that their religion and customs were superior to the religion and customs of the Hebrews. Yet through the very humiliations that Israel's departure from Him had invited, God gave Babylon evidence of His supremacy, of the holiness of His requirements, and of the sure results of obedience. And this testimony He gave, as alone it could be given, through those who were loyal to Him. PK 479.2"
"Now therefore, what have I here, saith the Lord, that my people is taken away for nought? they that rule over them make them to howl, saith the Lord; and my name continually every day is blasphemed."
Both passages address the idea of God's name being blasphemed due to the captivity of His people. While not a direct quote, the theme of God's reputation being at stake is present in both.