The father of Lamoni confers the kingdom upon a son and renames his son. It is not unusual in many cultures for a king to take a regnal name upon assuming the throne and indeed this very practice can be documented for the Classic Maya based on the evidence of the glyphic texts. What is mildly interesting in this case is that the king adopts the name of the people rather than the people and land adopting the king’s name, as had been the case in the past. Name changes for peoples in the Book of Mormon tend to occur when there is a new dynasty head in a new location.
In this case, three events combine. First, a new people designates its different identity with the name Anti-Nephi-Lehi. Second, the fact that the regnal name is the same name creates a further separation between the old and the new. Nevertheless, the people of Anti-Nephi-Lehi apparently are still living in their original cities, with believers and nonbelievers as citizens of the same city. This situation dictates the third event, the creation of a new polity that must attempt to incorporate all, whether converted or not.
I hypothesize that, given the Mesoamerican context, ruling clans have converted. These clans are probably connected by intermarriage and other kinship links, since the cities of Nephi and Ishmael were ruled by father and son. Similar relationships may have existed in the other cities. The conversion of the ruling clan would alter the ruling structure for the entire city, but still allow for other clans to maintain different religious affiliations. This situation allows a change of governance (the accession of the new king) yet still have a population sufficiently unified and separate that they can move in a body to the land of Zarahemla.