Names are important. That's an idea that is somewhat lost on many people in today's culture. Parents nowadays choose names for their children that merely sound pretty or are unique. Seemingly gone is the art of naming a child for his or her intended destiny. The Bible, however, is full of the rich use of naming for conveying meaning for a life. Jacob, for instance, begins his life with a name that means 'Deceiver'; and it was one that was very appropriate for the boy who tricked both his father and his brother. Later on, he is given the name Israel, which means 'Wrestles with God'. This was perfectly illustrative of his own encounter with God as well as the combined experience of all those tribes who would later bear his name. And four times we read that God has given him the name Jeshurun - 'Upright' - speaking of the fact that God has justified him.
In the 62nd chapter of Isaiah, this naming of God's people gets thrown into high-gear with no less than ten different names being given for the people of God.
In verse 1, God begins speaking to Zion and Jerusalem - that mountain and city that were the symbol for God's presence with His people. Then in verse 2, He tells them that He will give them a new name. He says in verse 4 that they shall no more be called Azubah and Shemamah: "Forsaken" and "Desolate". The fact that they were called these things shows God's judgment against their sin and their absolute inability to do anything about it. All of the good names that God is about to bestow on His people come purely from His grace to completely undeserving sinners.
Verse 4 contines by saying, "but you shall be called Hephzibah ('My Delight Is in Her') and your land Beulah ('Married')." God will take delight in and marry His people not because they are beautiful - quite the opposite; they were Forsaken and Desolate! Rather, He will make them beautiful by His own electing grace, deciding that He will bless them rather than curse them (as they deserve). By His grace and for His glory He will take a hopeless and bankrupt people and make them His own.
Another four names are fired off in quick succession at the end of the chapter: "The Holy People", "The Redeemed of the Lord", "Sought Out", and "A City Not Forsaken" (verse 12). The final two are a complete reversal of the names "Forsaken" and "Desolate", but the first two give the glorious reason for the change os destiny. The people (and this whole passage refers to God's work in Christ's Church) have been made a Holy People precisely because they have been "Redeemed by the Lord".
Here's the truth behind the names: God takes people who are forsaken and desolate - absolutely and completely without recourse to save themselves - and He makes them to be holy so that He can delight in the them. And He does this through the redemption that was purchased on the cross when Christ drank the cup of God's wrath that was poured for us. And if we trust in this glorious Christ and His redemption, then it is at that cross where God takes away our name, "Sinner", and names us His "Saints".