Inspired by What is the significance of the name "Jesus"? and previous readings about the name, the interpretation of Yeshoua means Joshua in the Old Testament and Jesus in the New Testament.
What brought about this differences in interpretation?
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It's not an issue of interpretation, just the representation of the same name in different scripts. You point out correctly that Jesus' name (in Hebrew/Aramaic) was Yeshua. This is the same name of Moses' successor, "Joshua." The difference is that the name "Joshua" (coming from the Hebrew Bible) is a direct transliteration from Hebrew to English (as was pointed about above, the "Y" comes to English as a "J"), whereas the name "Jesus" comes to English from Hebrew through Greek
Iesu. The vowels are different, and the "s" at the end is just the Greek case ending.
Yeshoua is translated as Jesus as well as Joshua in the Old Testament, even in modern texts, ala the Book of Wisdom by Jesus Ben Sirach.
In the Greek text, the author is called "Jesus the son of Sirach of Jerusalem." (50.27) "Jesus" is the Anglicized form of the Greek name Ἰησοῦς, the equivalent of the Aramaic Yeshua, derived from the older Masoretic Hebrew Yehoshua`. So Sayth Wikipedia