The question relates to Jeremiah 23:5-6 where the prophet makes a Messianic prophecy about a new descendant of David. In the Hebrew text the word for English ‘LORD’ is the divine name YHWH, usually transcribed ‘Yahweh’ or ‘Jehovah’:
5 Behold, the days come, saith the Lord, that I will raise unto David a righteous Branch, and a King shall reign and prosper, and shall execute judgment and justice in the earth. 6 In his days Judah shall be saved, and Israel shall dwell safely: and this is his name whereby he shall be called, The LORD Our Righteousness. (Jeremiah 23:5-6 KJV)
It is difficult to see how that can be taken as an actual name, in the sense of an English nickname or surname. The idea of a ‘name’ in Hebrew, particularly prophetic names, is not the literal nickname or surname of an individual, but a title expressing an aspect of that person. In this case the quality of righteousness, “zedek”, with the ending “-enu”, ‘our’.
R. K. Harrison (Tyndale Commentary on Jeremiah, 1973, p.120) reads that Yahweh-Zedek-enu here means “the one who secures our vindication”, and that the future name “Yahweh-Zedek-enu” is in contrast to the failed king Zedekiah; “the righteousness of Yah”. In any case there’s no hint that it is a statement somehow equating the Branch to come with Yahweh himself. The meaning is perhaps clearer in modern versions.
5 “Behold, the days are coming, declares the Lord, when I will raise up for David a righteous Branch, and he shall reign as king and deal wisely, and shall execute justice and righteousness in the land. 6 In his days Judah will be saved, and Israel will dwell securely. And this is the name by which he will be called: ‘The LORD is our righteousness.’ (Jeremiah 23:5-6 ESV)
A comparison can be made with other prophetic names in the Old Testament. The most famous ones being the names in Isaiah; “Shear-Jashub” or ‘A remnant shall return” (Isaiah 7:3), “Maher-Shalal-Hash-Baz” or “make haste to plunder” (Isaiah 8:3) , “Immanuel” or “God with us” (Isaiah 7:14, 8:8) and “Pele-joez-el-gibbor-abi-ad-sar-shalom” or “Wonderful Counsellor, Mighty God, Eternal Father” (Isaiah 9:6). The two last ones of these four particularly attract attention as possible “Trinitarian” names of Jesus, or statements otherwise supporting the Trinity. (In regard to those names please click through to the separate discussion).
In conclusion here though, there is no indication that Jeremiah, or any other prophet, intended the readers to understand that the Messiah (Hebrew “anointed one”) would actually be God himself. The whole intention of Anoint-ed, indicates annointed by someone, in Messianic context clearly annointed by God. So “Yahweh Zedek-enu” does not really state any more or less than the angel Gabriel’s instruction to Joseph :
“She will bear a son, and you shall call his name Jesus, for he will save his people from their sins.” (Matthew 1:21 ESV)
The Hebrew name Jesus (or Joshua), means “Yah-saves”. Not greatly different from “Yah-our righteousness”. Yet no one would claim that Jesus bearing the name “Yah-saves” means that Jesus himself is Yah.