These people were standing in, that is, they were relying in, they were trusting in, the name of their bearers - both physically and spiritually. Physically, they bore the name of Israel. Spiritually, they bore the name of God. But God is complaining, here, that their actions did not live up to either the majesty of their physical or their spiritual names.
This is a warning, I think, both to physical Israel and to the Israel of God, as the church is very plainly pointed out to be in Galatians 6:16. If we, who have taken (or bear) the name of God, use the name of God in any way that denies the true meaning, or character of God - we are either breaking the third commandment or coming awfully close to breaking it, or we are on our way to doing so. And it is interesting that the prophecies contain very much revelation along this line.