Jeremiah 23:5 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 which they shall call him, THE LORD OUR RIGHTEOUSNESS.
Both Jews and Christians agree that this is about the messiah.
Jer 23:6 says that many unspecified people will call the name of the Messiah, Jehovah our Righteousness. That means that they will know the Messiah as this, as the LORD who is our righteousness. When the indefinite pronoun is used as the subject to call the name of someone, it means that name is what the person really is. The Messiah really is Jehovah our Righteousness.
Jeremiah 33:15 In those days, and at that time, will I cause the Branch of righteousness to grow up unto David; and he shall execute judgment and righteousness in the land.
16 In those days shall Judah be saved, and Jerusalem shall dwell safely: and this is what they shall call her, The LORD [is] our righteousness.
Jer 33:15 talks about the messiah very similarly to 23:5.
v16 says that many unspecified people will call the holy city "Jehovah is our righteousness". That means that the holy city is a testimony of Jehovah becoming our righteousness through the Messiah in 23:6. In 33:16 the word "name" is not there as it is in 23:6. That is not what she is, but that is her testimony.