Alma 23:15-17

15 Therefore, we have named all the cities of the Lamanites in which they did repent and come to the knowledge of the truth, and were converted.

16 And now it came to pass that the king and those who were converted were desirous that they might have a name, that thereby they might be distinguished from their brethren; therefore the king consulted with Aaron and many of their priests, concerning the name that they should take upon them, that they might be distinguished.

17 And it came to pass that they called their names Anti-Nephi-Lehies; and they were called by this name and were no more called Lamanites.

Why that name?

I heard once that a meaning for 'anti' is mirror image.

That works.