Name as Mission Statement
Across both Testaments, this is a name that states a claim about God rather than simply identifying a person. “Yahweh saves” is, in effect, a compressed sentence: it names the acting party (Yahweh) and the action (saves) in a single word. Read this way, every bearer of the name — Joshua son of Nun, Joshua the high priest, and Jesus of Nazareth — carries a name that makes a theological claim before the person has done anything at all.
Name Versus Title
It's worth holding two things apart that are often blurred in casual usage: Yehoshua/Yeshua/Jesus is a personal name, attested for multiple distinct individuals across the biblical record. Christ (Greek Christos, “anointed one,” equivalent to Hebrew Mashiach, “Messiah”) is a title or office, not a surname. The New Testament's own usage keeps this distinction more often than popular devotion does — “Jesus the Christ” being closer to the New Testament's own grammar than a compound name.
This matters for reading the name-studies on this site accurately: the etymological argument (“Yahweh saves”) is about the personal name Yehoshua/Yeshua/Jesus specifically. It is not, on its own, an argument about the title Christ or about messianic office, which rests on separate textual grounds.
“The Name Above Every Name”
Philippians 2:9–11 describes God giving Jesus “the name that is above every name,” such that every knee will bow at it. Interpreters differ on whether “the name” there refers to the personal name Jesus itself, to the title/office of Lord conferred in the passage, or to both together; this site does not adjudicate that debate, but flags it as a live question in the secondary literature rather than a settled point.
The two Joshuas, read together
Devotional and typological tradition has long noticed the coincidence of a priest named “Yahweh saves” being cleansed and crowned in Zechariah's vision, centuries before a New Testament figure of the same name is described as a priestly and royal savior in the New Testament's own terms (see, e.g., the priest-king language of Hebrews and Revelation). This is a resonance later readers have drawn out, not a connection Zechariah's or Matthew's text states explicitly.