Textual: The records found by Limhi's expedition are specifically mentioned (the 24 plates which are the Book of Ether). These were not the only plates given to Mosiah. The record of Zeniff, which probably included the record of Noah and Limhi as well, was given to Mosiah, who reads them to his people (Mosiah 25:5).
The naming of this record as the record of Zeniff, even though it encompassed the reign of three different kings, is analogous to the situation suggested for the Book of Lehi. The official lineage record would be named for the lineage ancestor, and the name of the "ancestor book" would not be changed until a change in dynasty, which is the explanation for the Book of Mosiah which begins a new dynasty and also contains the accounts of three kings (Mosiah 1, Benjamin, Mosiah 2).
Social: While Mosiah received the Limhites "with joy," they were also certain to have been a difficult task of integration. Since they were an entire community come complete with their own structures and experiences, they would probably remain together. Thus Mosiah is faced with finding a way to include a new city inside his jurisdiction. The Limhites would therefore probably be sent to add to a small population, or to begin a new location in the land of Zarahemla, but not specifically in the city of Zarahemla.
Translation: It is possible that the phrase "received them with joy" was formal phrase for the integration of one people in to another because we have virtually the identical phrasing when Alma's people come to Zarahemla: