(After their conversion and name change, God quit cursing them.)
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.
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 ... and the curse of God did no more follow them. Alma 23:16-18
Here's a youtube video that will tell you the whole story of the Anti-Nephi-Lehies