Let them praise thy great and terrible name - The word rendered “terrible” means “to be feared or reverenced;” that is, his name - his being - he himself - is suited to inspire awe and reverence. The word “them” here refers to the nations over whom God reigns. It is a call on them to praise their king and their God.
For it is holy - See the notes at Isaiah 6:3; notes at Revelation 4:8. The fact that God “is” holy - that he is pure and righteous - that he cannot look upon sin but with abhorrence - is a just foundation for universal praise. Who could worship or honor a God who was not pure and holy?