Rabbi Nachman of Breslov: The name Moshe stands for Machloket Shammai v'Hillel - the dispute of the schools of Shammai and Hillel.
(יז) כָּל מַחֲלוֹקֶת שֶׁהִיא לְשֵׁם שָׁמַיִם, סוֹפָהּ לְהִתְקַיֵּם. וְשֶׁאֵינָהּ לְשֵׁם שָׁמַיִם, אֵין סוֹפָהּ לְהִתְקַיֵּם. אֵיזוֹ הִיא מַחֲלוֹקֶת שֶׁהִיא לְשֵׁם שָׁמַיִם, זוֹ מַחֲלוֹקֶת הִלֵּל וְשַׁמַּאי.
(17) Every argument that is [for the sake of] heaven's name, it is destined to endure. But if it is not [for the sake of] heaven's name -- it is not destined to endure. What [is an example of] an argument in the name of heaven? The argument of Hillel and Shammai.
שלש שנים נחלקו ב"ש וב"ה, הללו אומרים "הלכה כמותנו" והללו אומרים "הלכה כמותנו." יצאה בת קול ואמרה
"אלו ואלו דברי אלהים חיים הן, והלכה כב"ה
." וכי מאחר שאלו ואלו דברי אלהים חיים, מפני מה זכו ב"ה לקבוע הלכה כמותן? מפני שנוחין ועלובין היו ושונין דבריהן ודברי ב"ש ולא עוד אלא שמקדימין דברי ב"ש לדבריהן
For three years, the House of Hillel and the House of Shammai argued. One said, 'The halakha (law) is according to our position,' and the other said, 'The halakha is according to our position.'A heavenly voice spoke:"These and those are the words of the living God, and the halakha is according to the House of Hillel."A question was raised: Since the heavenly voice declared: "Both these and those are the words of the Living God," why was the halacha established to follow the opinion of Hillel? It is because the students of Hillel were kind and gracious. They taught their own ideas as well as the ideas from the students of Shammai. Furthermore, they even taught Shammai's opinions first.
Marc-Alain Ouaknin, The Burnt Book, p. 84
The Talmud says of Talmudic discussions: "The words of one and the words of the other are the living words of God. This statement should be seen as conditional: If there are words of one and words of the other, then they are words of the living God, and as a result, are living words.
(ג) אע"פ שנחלקו ב"ש [כנגד ב"ה] בצרות [ואחיות] ובספק אשת איש ובגט ישן [והמקדש את האשה] בשוה פרוטה [והמגרש] את אשתו ולנה עמו בפונדק לא נמנעו ב"ש לישא [נשים] מב"ה ולא ב"ה מב"ש אלא נהגו האמת והשלום ביניהן שנא' (זכריה ח) האמת והשלום אהבו.
Even though Beit Shammai and Beit Hillel disagreed concerning co-wives, sisters, the married woman, a supernatural write of divorce, the one who betrothes a woman with an object worth a perutah, and the one who divorces his wife and spends the night with her in an inn - Beit Shammai did not refrain from marrying women of Beit Hillel, and Beit Hillel from Beit Shammai. Rather, they behaved toward one another truthfully and there was peace between them, as it is said: "they loved truth and peace." (Zechariah 8:19)
Mikdash Melech to Zohar Parshat Bereishit 17b
In the time of the Messiah, we will follow the law according to Shammai. Hillel represents kindness and Shammai severity (hence the rulings of Beit Hillel are almost always more lenient). When the Messiah comes the advantage of the severity will be revealed and therefore the law will be in accordance with Beit Shammai. Beit Shammai comes from such a high level this present world is incapable of withstanding it, and only when the Messiah comes will we be able to follow their opinion.