It would be called the Josephites, after the region where the monastery would be located:
The valley of Josaphat in Israel (where tradition holds Christ will come at the end of the world, and the Judgment will take place):
Joel 3:2, 3:12:
"I will gather together all nations, and will bring them down into the valley of Josaphat: "Then I will enter into judgment with them there", on behalf of my people and for My inheritance Israel, whom they have scattered among the nations and they have divided up My land."; "Let the nations be roused; Let the nations be aroused And come up to the Valley of Jehoshaphat, for there I will sit to judge all the nations on every side.”