Brian Palmer in Slate investigates Jesus' name:
Christ's given name, commonly Romanized as Yeshua, was quite common in first-century Galilee. (Jesus comes from the transliteration of Yeshua into Greek and then English.) Archaeologists have unearthed the tombs of 71 Yeshuas. The name also appears 30 times in the Old Testament in reference to four separate characters—including a descendent of Aaron who helped to distribute offerings of grain (2 Chronicles 31:15) and a man who accompanied former captives of Nebuchadnezzar back to Jerusalem (Ezra 2:2).
The long version of the name, Yehoshua, appears another few hundred times, referring most notably to the legendary conqueror of Jericho (and the second most famous bearer of the name). So why do we call the Hebrew hero of Jericho Joshua and the Christian Messiah Jesus? Because the New Testament was originally written in Greek, not Hebrew or Aramaic. Greeks did not use the sound sh, so the evangelists substituted an S sound. Then, to make it a masculine name, they added another S sound at the end. The earliest written version of the name Jesus is Romanized today as Iesous. (Thus the crucifix inscription INRI: "Iesus Nazarenus Rex Iudaeorum," or "Jesus of Nazareth, King of the Jews.")
The initial J didn't come until much later. That sound was foreign to Aramaic, Hebrew, Greek, and Latin. Not even English distinguished J from I until the mid-17th century. Thus, the 1611 King James Bible refers to Jesus as "Iesus" and his father as "Ioseph." The current spelling likely came from Switzerland, where J sounds more like the English Y. When English Protestants fled to Switzerland during the reign of the Catholic Queen Mary I, they drafted the Geneva Bible and used the Swiss spelling. Translators in England adopted the Geneva spelling by 1769.
In contrast, the Old Testament was translated directly from the original Hebrew into English, rather than via Greek. So anyone named Yehoshua or Yeshua in the Old Testament became Joshua in English.
But there's another factor in separating Jesus from Joshua: Jesus isn't a Jewish name. Its a European Protestant form of the name. Joshua, on the other hand, sounds more Jewish. Joshua, or in its full form, Yehoshua, is a theophoric name that begins with the divine name YHWH. Perhaps in the 1st century this name carried the connotation of hope for divine deliverance from Roman oppressors.