I am the Lord - I am Yahweh. Here is also a change in the address. In the previous verses, God had addressed the Messiah. Here he turns to the people, and assures them that he is the only true God, and that he will not suffer the praise that is due to him to be given to any other, or to any graven image. The name Yahweh signifies being, or essential existence (see the note at Isaiah 1:9). It is a name which is given to none but the true God, and which is everywhere in the Scriptures used to distinguish him from all others.
That is my name - That is the name which I have chosen by which to distinguish myself from all idols, and which I regard as appropriately expressive of my existence and perfections. Thus it is used in Psalms 83:18 (compare Psalms 96:5). “And my glory.” The glory, honor, or praise that is due to me.
Will I not give - I will not allow it to ascribed to another; I will not allow another to assume or receive the honor which is due to me.
To another - To any other; whether it be man, or whether it be an idol. God claims that all appropriate honors should be rendered to him, and that men should cherish no opinions, maintain no doctrines, indulge in no feelings, that would be derogatory to the honor of his name. This declaration is designed to counteract the propensity everywhere manifest to attribute to man that which belongs to God, or to ascribe to our own wisdom, skill, or power, that which he alone can accomplish.
Neither my praise - The praise which is due to me. He would not permit graven images to receive the praise of having done that which he himself had accomplished.