Rabbi Nachman of Breslov: The name Moshe stands for Machloket Shammai v'Hillel - the dispute of the schools of Shammai and Hillel.
וההיא דפ"ב דשבת (דף לא.) ההוא דאתא לקמיה דהלל ואמר גיירני ע"מ לעשות כ"ג בטוח היה הלל דסופו לעשות לשם שמים
Tosafot ad loc.
But in the second chapter of Shabbat there is the one who came to Hillel and asked to be converted on condition that he be made high priest. Hillel was certain that it would ultimately be for heaven’s sake.
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.