“Thou shalt not take the name of the LORD thy God in vain; for the LORD will not hold him guiltless that taketh his name in vain.” - Exodus 20:7.
“Hallowed be thy name” is the next line in the prayer. The name which God Almighty took exclusively to Himself is JEHOVAH. Which means self-existing One or One Who lives of Himself uncreated. He lives from everlasting to everlasting. The name should be hallowed, meaning that it should be held in awe or deep reverence, and should not be used carelessly. (See Psalm 111:9) There are many people today who, contrary to the law of God, go to law courts and swear falsely in God's name. He would punish all such ones except they repent. In any case, Christians are not to swear anymore. - Matthew 5:33-37.
Another aspect of the matter is that we should not do anything that will make people to speak ill of or bring reproach to the name of God and His work (Romans 2:20-24) A high standard of morality or righteousness is expected from those who have given themselves to the service of God. Indeed, man was created to show forth the praise of God. (Isaiah 43:21) By sincere and faithful service, true worshippers give honour to God and hallow His name for their blessing by His grace. Jesus Christ stated: “Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven.” -Matthew 5:16.