It is typical for a king to declare himself formally. In this case, Limhi identifies himself by citing his lineage. He makes an explicit connection with the land of Zarahemla, because that is most likely the source of ultimate authority. Limhi does not, apparently, know that his captives are also from Zarahemla, so his statement to Ammon is not one of recognition of commonality but rather his assertion of authority.
This practice is also known from later Mesoamerican records. Those who moved from one area to another recapitulated their link to a remote but established lineage. The Cakchiquel specifically received their authority from Nacxit, the ruler in Tollan: “The Lord Nacxit said: ‘Climb up to these columns of stone, enter into my house. I will give you sovereignty.’” Neither the “Popol Vuh” nor the “Title of the Lords of Totonicapan” for the Quiché mentions sovereignty directly, but both trace their foundational lineages to events in Tollan. Tollan is “the place of cattail reeds” and is either a mythical place of origin or a designation for a particular people and place (Tula, Hidalgo) that was populated from around 700 A.D. to 1200 A.D. during which time it grew to become the dominant power in Central Mexico and influenced much of Mesoamerica. In spite of the similarity in name, all Mesoamerican descriptions of Tollan do not refer to the later city of Tula (Hispanicized version of the Nahuatl Tollan). Even before the references cited for the Cakchiquel and Quiché, Maya cultures would invoke Tollan as the source of their authority. In the earlier times, the reference was not Tula but Teotihuacan. However, the reference to authority was the same. David Stuart, an epigrapher from the Peabody Museum of Harvard University noted: “I… argue that Maya rulers kept open a claim to this earlier history, evoking Teotihuacan as both a place and an idea of political origin. This discussion [is] based in large part on my earlier decipherment of the Classic Maya name for Teotihuacan, ‘Place of Cattails,’ (equivalent to Nahuatl Tollan).”
Reference: See “Excursus: “The Voice of the People,” following Mosiah 29.