In historical documents that suggest that everyone did one thing, or that all members of another group did something else, we should understand that the actual historical example was not as exclusive as the statements would indicate. Thus, it is probable that at least some Amalekites and Amulonites might have been converted. It is probable that in the lands mentioned in Alma 23:9–12 there were some who were not converted. The specifics and the details of those conversions and non-conversions are not the point of the text. What is important in the writing of the story is that there was a division between those who did convert to the Nephite religion and those who did not. That was a fact, and it was a critical fact.
In the writing of the story, while the writer (Alma or Mormon, as there is no real clue as to who wrote these verses) does mention unconverted Lamanites, it is the Amalekites and the Amulonites who are mentioned first. Perhaps Mormon’s emphasis on the role of apostate Nephites would suggest that it is Mormon writing this section.
It is also part of the history that the overking names one of his sons as his successor. That son had also been converted, and he took the name Anti-Nephi-Lehi. Thus, there was a people with that name, and a king who took that as his throne name. This sets up a major conflict between those who were converted and represented by the king, and those who had not been converted and who were determined to claim the kingship through war against Anti-Nephi-Lehi and his people who had taken that name.