It goes without saying that the name God chose to give His Son is significant. The name given to the Incarnate Son of God is indicative of the mission on which God the Father sent Him to earth (Mat 1:21; cp. John 1:29, 3:17). The angel made this announcement to Joseph whose betrothed wife, Mary, had conceived a child of the Holy Spirit, “She will bear a son, and you shall call his name Jesus, for he will save his people from their sins” (Matthew 1:21).
The Second Person of the Holy Trinity Who had existed from all eternity became flesh, that is a human, in order to save His people from their sins. Joseph would probably have understood “His people” as a reference to the people of Israel. That understanding is probably too broad in that God has not chosen to save every Israelite, but only a remnant of them (Rom 9:6-8, 11:1-5). On another level, Joseph’s understanding of “His people” may also have been too narrow in that God is adding to the elect remnant of Israel, Gentiles who are called by His name. So, ultimately “His people” is a reference to all His elect people. It is these people, His people, Jesus came to save.
How can a person know that he is included in the people of God? Those who repent of their sins, believe that Jesus is the Son of God, and believe that He died for their sins and rose again from the dead are included among God’s people. Trust Him today as your Lord and Savior!