The etymology of the original name for "Jesus" is Hebrew in origin: The original Hebrew form is Y'-Sh-U-A, or Yeshwa יֵשׁוּעַ . Hebrew, specifically, Jewish etymology uses names to convey a message. Hence, when looking (for example) in a "name dictionary" for the meaning of specific names, you will find that names of Jewish origin consist on small messages.
According to Isaiah 26:1, 18 the name YESHWA means "that which is delivered, safe". However, there has been plenty of argument as far as how this meaning has been actually translated. What is, indeed, accepted is that Yeshwa may be shorter version of the name Yehoshua, or Joshua. If this is the way the name is intended to be used, then the name "Joshua" means "God saves", or "Yahwe is the way to salvation."
Now, the name of Jesus (Matthew 1:21), as we know it, has a Greek origin that has undergone a number of changes resulting from the processes of, either, translation (interpreting the meaning or content of a word) or transliteration (which focuses in the form, shape and sounds of the word, yet, not on the meaning).
"you shall call his name Jesus, for he will save his people from their sins" (Matthew 1:21)
Regardless of tits meaning, the Greek translation of the name of Jesus does not seem to have undergone dramatic changes, from the Greek "Iesous" or "Ihsous", to how we know it today. Yet, the complexity of Hebrew still creates the doubt that there may have been a transliteration of some kind in the process of putting the name of Jesus from the Hebrew Y'-Sh-U-A (Yod-Shin-Vav-Ayin) into the name of Iesous in Greek.
Interestingly enough, although the common Greek, also known as Koine Greek, was a language spoken by some during Jesus's time, it is more than likely that Jesus, himself, spoke one of seven dialects of Aramaic. Hebrew, ironically, was less-commonly used by the masses, to which Jesus belonged, than Hebrew itself.
Read from the links below the one on "The Holy Name of Jesus" from the Enotes resources for you to get even further information.