Exclusive Psalmody (EP) is a doctrine that has been adopted by some historically reformed churches. In brief, EP adherents claim that the 150 Psalms of the Old Testament (OT) are the only Biblically warranted songs allowed in worship. This supposedly aligns with the reformed Regulative Principle of Worship (RPW) that is summarized as "if commanded, required - if not commanded, prohibited".
The EP adherent claims that because there is (arguably) nowhere in the New Testament (NT)/New Covenant (NC) commanding the composition of new songs for use in worship, then songs that are written outside of the Bible (so called "uninspired" songs) are prohibited, thus only the inspired songs of the Psalms are proper and allowed in worship.
In contrast, Inclusive Psalmody (IP) acknowledges that while the Psalms are an incredible resource for sung worship, the church is also edified by the use of newly composed hymns and other spiritual songs, much in the same manner as newly composed prayers and sermons. (With the obvious acknowledgement that not everything newly composed is edifying and should be subject to the 1 Thessalonians 5:21 rule with Scripture as the prime source of evaluation.)
There are many arguments for and against EP, but I believe the strongest EP counterargument is the fact that EP implicitly prohibits the NT revealed name of Jesus in sung worship.
The EP position is that the word yeshua/ישוע is used many times in the Psalms and it is the root source of the name of Jesus. That is 100% accurate. However, they go on to assert that this satisfies any requirement concerning the use of Jesus' name in sung worship. The complication arises when the context of the word in the Psalms is considered. It is always used to speak of salvation, not the name of the One who is the revealed source and author of salvation, namely Jesus. EP uses theological/linguistic gymnastics to support a false conclusion.
The OT, including the Psalms, only speak of Jesus in "types and shadows", not directly using His revealed NT name. To rightfully sing of Jesus as Lord and Savior, one must sing incorporating the proper name of Jesus (i.e., Joshua, Yeshua, Ἰησοῦς, ישוע) to refer to the revealed Jesus, which the Psalms do not do.
This is not to imply that the Psalms are not to be used, or that Jesus' name be inserted into every element of worship constantly. It is to point out, again, that EP, by its very nature, never allows the revealed proper name of Jesus in sung worship.
I have compiled some references and uses of our Lord and Savior's revealed proper name to illustrate how EP is an erroneous doctrine. Keep in mind, this is in no way an exhaustive study concerning the name of Jesus, just some powerful examples (all from ESV - emphasis mine).
Our Lord refers to benefits of His revealed name:
John 14:13 - "Whatever you ask in my name, this I will do, that the Father may be glorified in the Son."
Matthew 18:20 - "For where two or three are gathered in my name, there am I among them."
At Saul/Paul's conversion, the Lord announces Himself by His revealed name:
Acts 9:4-5 - And falling to the ground, he heard a voice saying to him, "Saul, Saul, why are you persecuting me?" And he said, "Who are you, Lord?" And he said, "I am Jesus, whom you are persecuting.
The NT authors held the revealed name of Jesus in very high regard and its use as integral to the proper practice and worship of the church.