One of the most pathetic, yet widely popular, arguments against Exclusive Psalmody is that “singers can’t sing the name of Jesus.” In essence, it is pure mysticism:

“First, nowhere in the Bible are we commanded to sing the name ‘Jesus’. If God preferred the name Jesus over other biblical designations for our Lord (e.g., Immanuel, Yahweh, Lord, Savior, Jehovah Tzidkenu [cf. Jer. 23:5-6], the Prince of Peace, Messiah, the Lamb of God, the Son of God, the Son of Man, etc.), then He would have revealed His will concerning this matter to us in the Bible.

“Second, it is not the word ‘Jesus’ that we are to serve, exalt, worship and glorify, but what or whom the name points to or represents. There is nothing intrinsically sacred, mystical or holy regarding the word ‘Jesus.’ We respect the word and do not use it in an irreverent manner because of the Person behind the name. Bible scholars recognize that even the biblical expression in the name refers to a recognition or acknowledgment of the person who is named.When Paul says, ‘that at the name of Jesus every knee should bow’ (Phil.2:10), he refers to a recognition of the power, authority and majesty of Jesus. Matthew Henry writes, ‘At the name of Jesus; not at the sound of the word, but the authority of Jesus; all should pay a solemn homage.And that every tongue should confess that Jesus Christ is Lord—every nation and language should publicly own the universal empire of the exalted Redeemer, and that all power in heaven and earth is given to him, Matthew 28:18.’

“Since the Psalms eloquently and thoroughly recognize the power, authority and majesty of Christ as well as define His character and ministry, they exalt His glorious name because they exalt His person. To ignore this point and demand the use of the word ‘Jesus’ in singing praise is superstitious and irrational.” ~Brian Schwertley

Dr. Richard Bacon complied a list of Psalms that have the name of the Messiah in them:

YShU`AH in the following Psalms:
Psalm 3:8; 9:14; 13:5; 14:7; 20:5; 21:1, 5; 35:9; 38:22; 40:10, 16; 50:23; 51:14; 53:
6; 62:1, 2, 6; 68:19; 69:29; 70:4; 71:15; 74:12; 78:22; 88:1; 89:26; 91:16; 96:2; 98:2, 3; 106:4; 116:13; 118:14, 15, 21; 119:41, 81, 123, 155, 166, 174; 140:7; 144:10; 149:4.

You can sing Mashiach in Psalm 2:2; Psalm 18:50; Psalm 20:6; Psalm 28:8; Psalm 45:7 (verbal variant); Psalm 84:9; Psalm 89:20 (verbal variant); Psalm 89:38; Psalm 89:51; Psalm 105:15; Psalm 132:10; Psalm 132:17.