A reminder at the beginning of your study on this Isaiah text is helpful. Interpreters of Isaiah from every contemporary theological perspective recognize that Isaiah is a book from different historical periods. Usually it is thought that Isaiah 1-39 is mostly from the 8th century Judean prophet and often referred to as First Isaiah. The enemy in First Isaiah is more focussed on Assyria. Isaiah 40-55 is called Second or Deutero Isaiah attributed to a prophet in the Isianic tradition usually thought of as one who lived in Babylon during the 6th century. Here the enemy is far more Babylon. Isaiah 56-66 is called Third or Trito Isaiah, a collection of one or more prophets who lived in Judah after the return from the Babylonian exile. The enemy here may well be a people falling short in so many ways but desiring the salvation offered.
Despite the different historical periods all of the parts of the book share many common elements. There are adaptations, reversals, and responses to issues raised in these different historical periods. However the unity comes in common theological traditions. The vision of God as the king in the Davidic sense or adapted to the Davidic ideal is stressed. The holiness of God carries through these various parts. While First Isaiah largely consists of judgments the latter two sections are more focused on consolation and the demands of salvation. Second Isaiah's soaring images of hope do not get completely fulfilled in Third Isaiah's time.
Specific to Isaiah 62:1-5
One of the first questions that needs some answer regards the speaker of Isaiah 62:1. Certainly the prophet speaks but is God the one who declares, "I will not keep silent" or is it the prophet? Certainly the prophet is speaking but is he speaking the words of the LORD or is this his own prophetic voice?
However that question is answered it is clear that as we listen to this text in the church today we can understand that Jerusalem is given new names (Isaiah 62:4). Those names are filled with hope, "Hephzibah (My Delight Is in Her, meaning Jerusalem) and "Beulah" (Married meaning Jerusalem and the people are brought together again). [Side note: the song "Beulah Land" was probably stimulated by this text. So from Jerusalem one could see heaven.]
The implication in the Isaiah text is that just as the exilic returnees seek to no longer bear their names of Azubah (Forsaken) or Shemamah (Desolate) so we hope to find our salvation in these new God given names. We no longer want to make a name for ourselves (Genesis 11:4), we want to make a name for God, as the children of God.
In this Epiphany season the light that breaks forth in this text is one that opens us to serve anew. May we break away from our wayward ways so that we become a people bringing all of God's promises to fruition. Only then will we be a "crown of beauty in the hand of the LORD" (Isaiah 62:3) and God will rejoice over us (Isaiah 62:5).