Augustine of Hippo

The second commandment: "You shall not take the name of the Lord your God in vain; for whoever takes the name of the Lord his God in vain will not be purified." The name of the Lord our God Jesus Christ is Truth: he himself said, "I am the truth." So truth purifies; futility defiles. And because whoever speaks the truth speaks from what is God's—for "whoever speaks falsehood speaks from what is his own"—to speak the truth is to speak reasonably, whereas to speak futility is to make a noise rather than to speak. …

Sermon 8.5 ↗

Thomas Aquinas

This is the Second Commandment of the law. Just as there is but one God whom we must worship, so there is only one God whom we should reverence in a special manner. This, first of all, has reference to the name of God. "You shall not take the name of the Lord your God in vain." "In vain" has a threefold meaning. Sometimes it is said of that which is false: "They have spoken vain things every one to his neighbor" [Ps 11:3]. …

Explanation of the Ten Commandments ↗

Bonaventure

And from this fact, that He is the pious worshiper of Himself, the true witness to Himself, and the holy lover of Himself, there comes down from heaven a threefold radiation in the mind, according to the three commandments of the first tablet. For the creature must behave in relation to God in a manner that is pious, true, and holy. …

Collations on the Hexaemeron, Collation 21 ↗