When transliterating the name of Mashiach directly from Hebrew, instead of through Greek, it is the common practice today to use the form of the name which is found also in Aramaic, "Yeshua", instead of the form of the name which is found only in Hebrew, "Yehoshua". A common argument for doing this is that it is easy to imagine that "Yeshua" was the more common form used in Judea in the time when Mashiach lived upon the earth. In any case, it is said, all agree, it is the same name, whether in its longer or shorter form.
What is most important is to ask what form of the name God desired Mashiach to be known by. What was the form of the name with which the angels stated that the child should be called? Why does it matter? To try to put this into English, Strong's Concordance has:
ְהוֹשׁוּעַ Yhowshuwa` Jehoshua יְהוֹשֻׁעַ [Yhowshua]; from יְהוָֹה [Yhovah ] and יָשַׁע [yasha` ]; Jehovah-saved; Meaning: Joshua or Jehoshua = "Jehovah is salvation" .
It is clear that the contemporary English letter, "Jay" does not accurately transliterate the Hebrew, "Yod". There are also transliteration issues for the letter "Vav" and for the vowel sounds. But apart from this, the meaning is accurate: "Yehoshua" means "Hashem is salvation".
While the form of the shortened form of the word, "Yeshua", can have this same meaning if it is understood just as an abbreviation of this name, the word, "yeshua", also simply means "salvation", in the sense that follows from the literal meaning of the word, which is, "he is saved". It is possible that some people like to think that the angels conveyed the command that his name should be called "Yeshua", because they want to understand that this says that he is himself salvation, that in his salvation from death the world would be saved, and that God was telling the world that this would be the case.
In his own words, however, it was the message of Yehoshua that he was come to reveal the Father, to reveal who is the true God and Creator, the God of Israel, not to bear witness to himself. The longer form of the name, "Yehoshua", is fully consistent with this message.
Again, it is important to clarify that while the shorter form of the name might be used by someone with a theology that could obscure Mashiach's purpose, his purpose of bringing the final revelation of the Father of Israel as the one true and only God, this does not mean that the shorter form of the name is not also his name. It is. And there is much that can be learned from both forms of his name. However, I believe that as much as it is revealed to anyone that he has saved his people, Israel, from their sins, that much it will also be revealed to them once and for all that Hashem is the savior of Israel, is one, and that the name of Mashiach should be called, Yehoshua.
Following is some enlightening midrashic material from the Talmud that provides a deep background for this understanding.
When the Almighty gave Torah to the Jewish People, He gave them positive and negative commandments. God gave additional mitzvot to a Jewish king, as it states, "He should not accumulate many horses, [or] silver and gold.. he should not have many wives lest his heart turn aside." King Solomon arose and considered himself wiser than God's decrees. He said, "Why did God give the command not to have numerous wives? It seems to be because of the continuation of the verse, 'lest his heart turn aside.' I will have many wives, and my heart shall not turn aside."
Our Sages said: at that time, the letter , from the word ירבה [many] ascended and prostrated itself before the Almighty. It said, "Master of the Universe, did You not say that no letter of the Torah would ever be nullified? Yet Shlomo has nullified me! Today he will abolish one letter, and tomorrow another, until the entire Torah will be abrogated."
The Almighty replied, "Let Shlomo and a thousand like him be nullified, yet not one crown (from on top of the yod) will be abolished!"
From where do we see that it was removed from the Torah and yet subsequently returned? It states, "Sarai your wife will no longer be called Sarai, but Sarah." Where did it return? "Moshe called Hoshea, the son of Nun, Yehoshua...
The tractate Termurah was composed in Talmudic Babylon (c.450 - c.550 CE). Temurah (Substitution) belongs to the fifth order, Nezikin (The Order of Damages) and discusses the laws of what happens if an animal is substituted for an animal dedicated for a sacrifice.
As Yehoshua said:
For truly I say unto you, Till heaven and earth pass, one yod or one crown of a yod shall in no wise be nullified from the Torah, till all be fulfilled.
Did Yehoshua quote the Oral Torah that was taught in his day and later written down in the Talmud? Or did the Oral Torah here quote his saying? In either case, it is one teaching.
And it can be found most edifying that the teaching as elaborated in the Talmud applies this very teaching to the account of how the name of Yehoshua came to be created by divine inspiration by Moshe and is recorded in the Torah of Moshe.
Reference material: Irving M. Burnim - Sabbath Seder - 0n Sefer Devarim / Vezoth Haberachah
pp. 482-483
Additional Resources
Yehoshua’s Transformation
The Torah states, “And Moshe called Hoshea Bin Nun ‘Yehoshua.’” The Midrash explains that Moshe added the letter “yud” to Hoshea’s name because this letter connotes the Name of G’d (Yud Kay). Meaning, “G’d (Ka) should come and save you.’” Rashi explains that Moshe prayed that Yehoshua should be protected from the evil plotting of the spies. Ohr HaChaim HaKadosh asks, “Why did Moshe need to add the letter ‘yud’ to Hoshea’s name? One would think that Moshe’s supplication on his behalf would have been sufficient to protect him.” Ohr HaChaim HaKadosh answers that it was necessary for Moshe to add the letter “yud” to Hoshea’s name because the Name of G’d needed to be integrated into his name. The letter “yud” has the numerical value of ten, and thus was necessary to counter the influence of the ten spies.
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