The name Noah is mentioned twice in this verse. Why would Zeniff name his son Noah? Let us assume that Noah was born in the City of Nephi, which makes sense chronologically.
When parents in the Nephite culture gave a royal son a name like this, they were probably hoping that he would be like Noah in a positive sense. Noah had cried repentance, and King Noah’s father, Zeniff, certainly would have appreciated that. In addition, Noah in Genesis was given a promise. After the flood, the rainbow symbolized God’s promise, "I will not destroy this land again" (Genesis 8:21–22, 9:14–15). God had given a new covenant; he started them over with a whole new world. Zeniff must have seen himself in this role as well: redeeming the land of Nephi and starting over. I wonder if King Noah thought of himself in that mode as starting over. And perhaps God’s ancient promise may have given him great confidence, which he turned into overconfidence. Perhaps he wrongly reasoned that, because God had promised his namesake that He would never again destroy the world by flood, he and his people could be confident that they would not be destroyed. But, unfortunately, he did not walk in the ways of his father, Zeniff, and he did not correctly keep the commandments of the Lord. As a result, tragedy befell him. He should have learned from his namesake, Noah of old, to heed the warnings and follow the commandments of the Lord, in spite of any false sense of security.
Book of Mormon Central, "How Does The Book of Mormon Use a Hebrew Pun on King Noah’s Name? (Mosiah 11:6)," KnoWhy 406 (February 8, 2018).
Matthew L. Bowen, "’This Son Shall Comfort Us’: An Onomastic Tale of Two Noahs," Interpreter: A Journal of Latter-day Saint Faith and Scholarship 23 (2017): 263–298.