“Jesus.” Jesus is the Greek form of the name “Joshua,” which means “Yahweh saves.” It was a common name at the time of Christ. The angel would have spoken to Joseph in Hebrew or Aramaic because the phraseology is Semitic,a and the name “Jesus” means “Yahweh is salvation.” The angel explains the name “Jesus” by saying, “for, he will save his people from their sins.” “Jesus” is the same name in Hebrew, Aramaic, and Greek, as “Joshua” in the Old Testament, something that has caused some confusion in some modern versions. For example, in the King James Version in Acts 7:45 and Hebrews 4:8, the Old Testament man Joshua is mistakenly called “Jesus.” Joshua was one of the types of Christ in the Old Testament and there are some profound parallels between Joshua and Jesus.
It should be noted that “Jesus” is the English name of the man Jesus, and the name is spelled and pronounced differently in different languages. In Hebrew the name is Yeshua or Yehoshua (the shorter and longer form of the name), in Greek the name is Iēsous (approximately pronounced Ē-ā-sous; Greek has no “Y” or “J”), in Latin the name was Iesus (from the Greek, and also approximately pronounced Ē-ā-sous), in English the name is “Jesus” (the letter “J” was invented for English in 1524), in French the name is Jésus (pronounced Jézu), in Spanish the name is Jesús (pronounced Hay-'soos). In some English-speaking Christian circles it has become fashionable to call Jesus “Yeshua,” but that is not “more holy” than using his name in the vernacular of one’s own language, thus “Jesus” in English. In fact, there is little doubt that when Jesus was alive on earth, the people around him (including his family, who were most certainly bi-lingual and likely even tri-lingual) called Jesus by different names depending on whether they were dominantly Hebrew (like many rabbis), Aramaic, Greek or Latin (like Pontius Pilate). Jesus knows his name and answers people who call out to him no matter how his name is spelled or pronounced in the language of the one calling to him.
“it is he.” This is emphatic in the Greek; “he” is put as the very last word in the sentence for emphasis. That would only be confusing in English, so we would have to use capital letters or bold letters. We might say, “Because HE will save his people from their sins.” We place a little more emphasis on it by saying, “it is he,” (cp. NASB).
“sins.” In this context, to be saved from sin is multifaceted. The major emphasis is a metonymy of effect, where “sin” is put for the effect of sin, i.e., the consequences of sin, which is death. In saving people from their sin, Jesus saves people from everlasting death. Jesus Christ came to give people everlasting life, as Scripture attests in many places. Also, however, Jesus saves people from sin in many other ways, including changing their life so that they do not continually live in sin and its consequences, and forgiving sin so people do not have the weight of sin on their shoulders.
[For more on sin, what it is, and what it does, see commentary on 1 John 1:7, “sin.”]