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
"Study to shew thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the word of truth. But shun profane and vain babblings: for they will increase unto more ungodliness" (2 Timothy 15-16).
LET IT BE KNOWN: That Israel is God's name. The Jews are the children of Jacob. It was Jacob whose name was CHANGED to Israel. The children of Jacob/Israel were the first race of people adopted into the family of God. When you adopt children you change their name. This is why those that are not of Israel (Gentile, Hamite's, Arab's etc) must become spiritual Israel in order to be adopted when Jesus returns.
"For as many as are led by the Spirit of God, they are the sons of God. For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father... For we know that the whole creation groaneth and travaileth in pain together until now. And not only they, but ourselves also, which have the firstfruits of the Spirit, even we ourselves groan within ourselves, waiting for the adoption, to wit, the redemption of our body" (Romans 8:14-23).
Even those whom were born Israelites in the flesh must become spiritual Israel to partake in the kingdom of God (they should be spiritual already since the law & the testimony came to Israel first). "For they are not all Israel, which are of Israel: Neither, because they are the seed of Abraham, are they all children..." (Romans 9:6-7)
"Israel hath not obtained that which he seeketh for; but the election hath obtained it, and the rest were blinded" (Romans11:7).
To Israel, "pertaineth the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises" (Romans 9:4)
So claiming to be a child of God, or Israelite and not doing what is required of you in the scripture is taking the name of the Lord thy God in vain.
Using the name of God in any frivolous manner is taking it in vain.
Swearing an oath in the name of God and not performing that which you swore is taking the Lord thy God's name in vain & he will not hold you guiltless. "When thou vowest a vow unto God, defer not to pay it; for he hath no pleasure in fools: pay that which thou hast vowed. Better is it that thou shouldest not vow, than that thou shouldest vow and not pay. Suffer not thy mouth to cause thy flesh to sin; neither say thou before the angel, that it was an error: wherefore should God be angry at thy voice, and destroy the work of thine hands?" (Ecclesiastes 5:4-6)
Affirming the truth of something obvious (due to its triviality) in the name of the Lord thy God is taking His name in vain.
The use of the name of God in a manner that would dishonor God is taking His name in vain.
To appropriate God's name for deceitful purposes or actions is taking his name in vain.
"For the LORD, whose name is Jealous, is a jealous God" (Exodus 34:14)
"The LORD thy God is a consuming fire, even a jealous God." (Deuteronomy 4:24)