According to Matthew 1:21, “Jesus” (in the form Iesous or Yeshua) means “he shall save.” Matthew also states that Christ fulfills the prophecy of Isaiah 7:14 – “And you shall call his name Immanuel, which translated means, God with us.”
In 1-2 Thessalonians, Paul also reveals how Jesus is the personal manifestation of Yahweh. The following is taken from my commentary on 1-2 Thessalonians, which includes a summar of the epistles’ doctrine. You can buy it from Logos, Amazon, Zondervan. Here is an interview I gave about it.
‘Paul knows well the power of myth to shape the self-understanding of both the individual and the community. In preaching Jesus, however, he does not simply ask people to replace old myths with new ones. Rather, he calls them to discard myth as a category of knowledge in favor of following one who died in a certain way at a recent time in Judea (1 Thess 2:15; 4:14) and was then resurrected (1:10; 4:14). In Paul’s theology, one cannot accept the ethical and existential features of the gospel without accepting its historical matrix.
‘For Paul, Jesus is “Lord,” the one to whom all the world is held accountable. Christians must follow his authority (1 Thess 4:1–2; 2 Thess 3:6, 12); his word is a divine oracle (1 Thess 4:15). But “Lord” does not simply mean someone with some sort of authority. Paul regularly mines motifs from the Scriptures, verses that spoke in the Hebrew of Yahweh, rendered in LXX as references to “the Lord”/κύριος. In his hands, these verses can be applied to the Lord Jesus. For example, when Jesus comes, people will be separated “from the presence of the Lord [Jesus] and his glorious might” (2 Thess 1:9). Paul’s language is taken from Isa 2:10, where Yahweh is the judge who inspires terror in the wicked.
‘In verse after verse Jesus and the Father interchange roles and actions. Although we modern Christians might not be fazed by this fact, its import would not have escaped Paul. The former Pharisee prayed to a crucified and resurrected man; he offered praise and thanks to the Son as he did to God the Father; he expected Christ to answer prayers as would the Father (cf. 1 Thess 3:11–13; 2 Thess 2:16–17). Paul, who had probably heard the Aaronic blessing of Num 6:24–26 every week of his life—“The LORD bless you and keep you; the LORD make his face shine on you and p 346 be gracious to you; the LORD turn his face toward you and give you peace”—now blesses the chosen people in the name of the Lord Jesus: “Now may the Lord himself, the Lord of peace, bestow on you peace at all times and in every way.… The grace of our Lord Jesus Christ be with you all” (2 Thess 3:16, 18). Jesus is Yahweh Sabaoth, Lord of the heavenly armies (2 Thess 1:7). He is the divine Avenger (1 Thess 4:6), the divine Savior (1:10).
‘In 1–2 Thessalonians, eschatology is key, and it is christocentric. This too might seem unremarkable for us who were raised to equate the end of the age with the second coming of Christ. Yet in Second Temple Judaism, the Messiah typically played a subordinate role in the final judgment. Eschatology consisted in the coming of God himself, who might also use a human Davidic king, or angels, or a heavenly Son of Man. But the focus was always on God, and the glorious epiphany was the coming of God. I have had cause to remark throughout this commentary that Paul may have taught the Thessalonians something like the Matthean Olivet Discourse. There too, Jesus’ teaching was focused on his own coming as the Son of Man. The kingdom of God comes, Jesus taught, but where is God himself when the age draws to a close? Paul follows neatly this line of thought, that God’s kingdom comes in and through Jesus.
‘Nowhere is this more apparent than in 1 Thess 3:13, which we have interpreted as “the coming of our Lord Jesus with all his holy angels.” Here Paul gives a clear nod to Zech 14:5—and perhaps Matt 24:31—as he applies a passage about Yahweh’s coming to Jesus: “Then the LORD my God will come, and all the holy ones with him.” The parousia of Jesus is the divine epiphany, at which he will kill the Man of Lawlessness (2 Thess 2:8). It is Jesus’ name that is glorified at his coming (1:12). The day of Yahweh from the OT prophets has been transformed into the day of the Lord Jesus Christ (see comments on 1 Thess 5:2). For the saints, eternity is defined as being forever with the Lord Jesus (4:17; see also 5:10; 2 Thess 2:1).’
“Paul agrees: Christ is Immanuel, God with us,” by Gary S. Shogren, Professor of New Testament, San José, Costa Rica
Open Our Eyes, Lord! 
Does Isaiah’s original intention with the Immanuel prophesy matter for interpreting what Matthew means by the name? In Isaiah Immanuel appears to be a sign-name given to a human king through whom God will alter Israel’s standing in the political arena. It’s purpose in Isaiah does not seem to be incarnational.
It’s a tricky issue, Alex, isn’t it. It’s important to deal with what Isaiah meant by his prophecy. Nonetheless, I don’t think we can limit ourselves to his understanding. In the same way, Joel could not possibly have comprehended that Joel 2:28-29 would be fulfilled in the church, thousands of years before the end of the age. So while I think we must take Joel or Isaiah seriously, we have to accept that Christ and the apostles are going to find a deeper or broader meaning. Hope this helps! Gary