At the time of His birth, the name was relatively common, about the same as it is in Hispanic cultures today. It comes from Ἰησοῦς (Iesous) which, in turn, comes from the common Hebrew name ישוע (yēšūă‘), a slightly simplified form of the name Joshua.
Names in the Bible often have significant meanings, especially this one. The angel Gabriel, when he told Mary she would bear a child, specifically told her to name the child Jesus. “And behold, you will conceive in your womb and bear a son, and you shall name Him Jesus.” (Luke 1:31)
The name means “salvation” and comes from the Hebrew verb meaning to rescue or deliver.
Joseph, too, was told to name the child Jesus. An angel of the Lord appeared to him in a dream and told him, “She will bear a Son; and you shall call His name Jesus, for He will save His people from their sins.” (Matthew 1:21)
There is an emphasis in the Greek of Matthew 1:21 that may not be clear in the English translation. It is not just that Jesus will save, it is that “He Himself” will save. In faith we receive this wonderful gift from Him, but salvation is accomplished completely and entirely by Him.
“For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; not as a result of works, so that no one may boast.” (Ephesians 2:8,9)