After reconfirming (and relocating) the Abrahamic covenant, the Lord reconfirms the Benjaminic covenant of the name. That covenant also moves from the people to the church. Where Benjamin's covenant defined a people, this covenant of name will define a segment of the people.
In both of these moves the Lord establishes in the New World what will not become a reality in the Old World for another perhaps 150-200 years. The diversity of population and government requires that the covenants become individualized rather than communal, and the Lord establishes that change here due to the diversity of the Zarahemla kingdom. That diversity will become more apparent in future chapters.