Isaiah 62
The New Name
2 And the Gentiles shall see your righteousness, and all kings your glory: and you shall be called by a new name, which the mouth of the LORD shall name.
Verse 2: a new name: this prophecy is linked to Acts
11:26
where the "disciples were called Christians first at Antioch."
And this
according to the prerequisites enumerated in this passage. The
conditions
are that Zion would be named:
1. A new name: Brothers, Disciples, Nazarenes, Holy
Ones, etc.
will not meet the criterion.
2. Called after the Gentiles had seen God's and Zion's
righteousness.
The conversion of the household of Cornelius, the first
Gentiles, is
the subject of Acts 10. Immediately in Acts 11, in the first
Gentile church,
the disciples are called Christians. They had not been called
Christians
from the day of Pentecost and following when only Jews and
Proselytes had
been converted.
3. The mouth of the LORD shall name. God must call the
name.
In this passage the words "shall name" is a verb: 
[yi(n)qqabenu]
a very specific word which means to specify, or appoint, or
designate.
It is not the simple word "call." 
[qora'] or
"name" 
[shem]. Thus also in Acts 11:26
the word
translated call is not the simple word "call" 
[kalein] but 
[chrematisai] which
means "to
be called by divine appointment" and corresponds exactly to
Isaiah 62:2.
Thus "Christian" meets all the criteria: 1. It was new when
called,
never before used. 2. It was not called until Gentiles became
part of the
renewed Zion. 3. God called it.
See also the important note under 65:15.
3 You shall also be a crown of glory in the hand of the LORD, and a royal diadem in the hand of your God. 4 You shall no more be termed Forsaken; neither shall your land any more be termed Desolate: but you shall be called Hephzibah, and your land Beulah: for the LORD delights in you, and your land shall be married.
Verse 4: Hephzibah: In Hebrew this is two words meaning "my delight is in her." and Beulah means "married."
5 For as a young man marries a virgin, so shall your sons marry you: and as the bride groom rejoices over the bride, so shall your God rejoice over you. 6. I have set watchmen upon your walls, O Jerusalem, who shall never hold their peace day nor night: you that make mention of the LORD, do not keep silence, 7 And give him no rest, until he establish, and until he make Jerusalem a praise in the earth.
Verse 7: Rest, Establish: The LXX considered the form
translated
"rest" to be the same word used in Gen 1:27 for "likeness" and
used the
form 
(homoios) meaning "image" or
"the same
as." The Hebrew form for "establish" 
(yekone:n)
is derived from the noun 
(kone:n)
which means
a settled place of God's sanctuary or holiness. The reading with
these
words in mind would be: "For my likeness will not be given to
him until
he establishes Jerusalem as a sanctuary and sets her as a prayer
of praise
in the earth."
8 The LORD has sworn by his right hand, and by the arm of his strength, Surely I will no more give your corn to be meat for your enemies; and the sons of the stranger shall not drink your new wine, for which you have labored: 9 But they that have gathered it shall eat it, and praise the LORD; and they that have brought it together shall drink it in the courts of my holiness. 10. Go through, go through the gates; prepare the way of the people; cast up, cast up the highway; gather out the stones; lift up a standard for the people. 11 Behold, the LORD has proclaimed to the end of the earth, Say to the daughter of Zion, Behold, your salvation comes; behold, his reward is with him, and his work before him.
Verse 11: Your salvation comes: Your salvation is personified in this passage. The antecedents of all the following pronoun suffixes refer to Your Salvation. It is referred to by "his reward," and "his work.". As a name "your salvation" is "your Yeshua," which of course is the Hebrew name of Jesus.
12 And they shall call them, The holy people, The redeemed of the LORD: and you shall be called, Sought out, A city not forsaken.