In the elongated form יְהוֹשֻׁעַ (Yehoshua) the yod-hah combination points to the name being theonymic, the truncated form of the Tetragrammaton, we find this usage frequently among Jewish and Hebrew names: Isaiah is Yesha'yahu, meaning "YHWH is salvation"; Elijah is Eliyahu, meaning "my God is YHWH", etc. Yehoshua, and its shortened form Yeshua mean "YHWH saves"; the Hebrew word for "salvation" is the feminine noun יְשׁוּעָה (yeshuah), which yes, does sound like "Yeshua", but they aren't the same word. Hoshea (הוֹשֵׁעַ) is the masculine, name form and it does, in fact, mean "salvation".
And the fact remains that we are talking about the Aramaic, not Hebrew. Jesus and His family didn't speak Hebrew, that wasn't the language of the family home in Nazareth; the language of the family home in Nazareth was Aramaic, as that had been regular, every day language of the Jewish people living in the region of Palestine since the Babylonian Exile where Aramaic was the lingua franca of the Babylonian Empire, and later, the Persian Empire. This is why a number of post-Exile books which make up the Old Testament are written entirely or in part in Aramaic, such as Esther and Daniel. The language Jesus spoke was Aramaic; and when Mary and Joseph addressed Him they would have spoken His name in the way normal for them as Galilean Jews; and that would have probably been something similar to "Yeshu'" or "Yisho'".
-CryptoLutheran