Zoram’s blessing was that he would dwell in safety and prosperity, as long as he remained aligned with Nephi. When Nephi, shortly after the death of Lehi, left the land of first inheritance, Zoram went with him. Thus, Nephi’s oath and promise to Zoram, made outside the walls of Jerusalem, that "you shall have place with us" (1 Nephi 4:34), was fulfilled. That promise was not made by Laman or Lemuel. Zoram was bound into this family because of Nephi, and Lehi honored Nephi’s bond.
The descendants of Zoram, the Zoramites, continue to be a separate tribe well into Nephite history. Zoram had been a servant to Laban, probably a soldier of some kind under Laban’s command. Thus, it is interesting and realistic that Lehi provided that Zoram’s seed would live in security with Nephi’s seed (1:32). Zoram was willing to go with Nephi, probably for a number of reasons, not the least of which were the terms of Zoram’s blessing. If he doesn’t stay with Nephi and doesn’t remain a "true friend" or ally of Nephi (1:30), the promises and his rights of inheritance in this confederation would be compromised and voidable, because those are the conditions upon which those blessings are given.
When they left, Nephi’s group was composed of Nephites, Jacobites, Josephites, and Zoramites. Jacob was given the temple, Joseph was made a teacher, and Zoram appears to become the military leader. Zoramites are mentioned many times in the Book of Mormon, but almost always in connection with military positions or affairs.
This was their tribal cast or their role in this society. Centuries later, Alma the Younger becomes worried because the Zoramites have left the Land of Zarahemla and have moved to the Land of Antionum. They have built their own city, they have withdrawn, and they have severed relationships with the Nephites. Alma the Younger will take a group of missionaries to go to preach to them. He wants to bring them back for spiritual reasons, but also because he is afraid that the Zoramites will form an alliance with the Lamanites (Alma 31:4), effectively renouncing Lehi’s arrangement set forth here in 2 Nephi 1.
Book of Mormon Central, "How is the Name Zoram Connected with Pride? (Alma 31:25)," KnoWhy 458 (August 14, 2008).