Cultural: The naming of something in the ancient world was very important. There are aspects of naming that are difficult for modern readers to understand because we use the name only as a label. The ancient world frequently used it as a definition. Names were who a person was. In many societies there is a name for the child as they are growing up, but they take on a new name when they become adults and are more sure of who they are. In the New World Book of Mormon we have already seen this naming phenomenon in king Benjamin’s address to his people. He urged a new name upon them as well. This new name for the Lamanite believers served a couple of functions. It separated them from both their past culture, and apparently their past political affiliations. It also united them even more tightly under the gospel, emphasizing their new similarity over the differences of cities from which they had come.
The name they selected reads strangely to our ears because of our understanding of “anti-“ as “against.” We have that understanding because of the particular language heritage of English, which would not have affected the Book of Mormon. In the Book of Mormon the provenance of “anti” would be very different, and therefore have a different meaning, even though it is identical to a form we use.
A suggestion apparently made by Hugh Nibley is that “anti” is related to a Semitic and Indo-European root that is related to “facing” as one might face a mirror, and thus might mean that they “mirrored” the teachings of Nephi and Lehi (Daniel H. Ludlow, A Companion to Your Study of the Book of Mormon. Deseret Book 1976, p. 209-10). While interesting, this etymology does not quite ring true in the Book of Mormon. In Alma 21:11 we find a village named Ani-Anti. That construction does not bear sufficient resemblance to Nibley’s suggestion to suggest that his understanding would be correct.
One of the aspects of the name that is possibly important is the Nephi-Lehi part of the name. Note that this is not the acceptance of the political label of Nephite. It very specifically includes Lehi in the formulation. It is possible that this has a somewhat genealogical intent, that is, to retain the connection of lineage through Lehi, but to adopt into the Nephi branch of that lineage. Another speculation might be that this body of people relocated to the village of Ani-Anti, and named themselves for that location. The problem with any of these speculations is that they are pure speculation. The answer is that we don’t know what the name meant.