Albert Barnes Commentary Ezra 5:1

"Now the prophets, Haggai the prophet, and Zechariah the son of Iddo, prophesied unto the Jews that were in Judah and Jerusalem; in the name of the God of Israel [prophesied they] unto them." — Ezra 5:1 (ASV)

Haggai and Zechariah stirred up Zerubbabel and Joshua (Ezra 5:2; Haggai 1:14), and warned the people against neglecting the building of the temple in order to give themselves to the beautifying of their own houses (see Haggai 1:4, Haggai 1:9). Zechariah was the son of Berechiah, and grandson of Iddo (see the marginal reference; Matthew 23:35). Compare a similar application of “son” in the case of Jehu (see the 2 Kings 9:20 note).

In the name of the God of Israel, even to them—Rather, “in the name of the God of Israel, which was upon them.” The two prophets addressed the Jews regarding their being God’s people, or, in Hebrew phrase (see the Jeremiah 15:16 margin), “having God’s name called upon them.”