Did God name Cyrus? Or, did He just identify Cyrus as the one to order Jerusalem rebuilt?
The prophet Isaiah lived c.740 BC through the reigns of Uzziah, Jotham, Ahaz, and Hezekiah. He was the one who prophsied Cyrus' role in rebuilding Jerusalem. Isaiah 1:1; 44:28; 45:1
Cyrus was the king of Persia who conquered Babylon c.539 BC and pemitted the Jews to return to their land in fulfilment of Isaiah’s prophecy.
Jeremiah had prophesied that the Babylonian captivity would last 70 years. Cyrus brought it to an end. 2 Chronicles 36:22,23
This is an example of God having intimate knowledge of the future. It does not mean that God actively caused the Persian to be named Cyrus, but rather that he knew, before he was born, what Cyrus’ parents would name him. Also that the Persians would have the opposite policy to the Babylonians concerning the conquered nations. They would repatriate them to their own lands. Isaiah 46:9,10
It is the fulfilling of prophecy that gives confidence that God is the author of the scriptures which make up the Bible.
I hope this helps,