We have part of the original manuscript here, but unfortunately we cannot be sure whether Oliver Cowdery wrote Ammon or Aaron. The first two letters of the name were at the end of a line, but that portion of the manuscript leaf is no longer extant. At the beginning of the next line, the last three letters of the name have some overwriting and are difficult to read. The n at the end of the name is fairly clear, but the o is very vague; worst of all, the first letter in this line can be either a defective m (with the second arch lower than the first) or a strange-looking re (with excessive rounding of the r). Oliver seems to have initially written the name in 𝓞 as Aaron, then corrected it to Ammon. If so, when he came to copying from 𝓞 into 𝓟, he almost made the same initial mistake of writing Aaron instead of Ammon. Oliver’s correction in 𝓟, unlike the one in 𝓞, is clear: he started to write Aaron by writing the first three letters, Aar; at that point he overwrote the second and third letters, ar, with an m and then finished producing the correct name, Ammon, by writing inline the rest of that name (the last three letters, mon). Thus ultimately Oliver interpreted the corrected name in 𝓞 as Ammon rather than Aaron.
Elsewhere in the text we have ten examples of “Ammon and his brethren” and seven of “Aaron and his brethren”. Here I exclude five instances of “Ammon and his brethren” where Ammon refers to the descendant of Zarahemla who found the people of Limhi (as described in Mosiah 7:3). I also exclude one unclear case involving both Ammon and Aaron:
In Alma 22–23, there is a division of missionary labor, with Ammon continuing to work with king Lamoni’s people and Aaron and his brethren working within the larger kingdom that was ruled by king Lamoni’s father. In this portion of the narrative, we have the following passage, just a couple of verses before Alma 23:6, where the narrative refers to “Aaron and his brethren”:
(The reading here is largely based on 𝓟; in this case, the name Aaron is not extant in 𝓞.) The passage then moves on to discuss (in Alma 23:6) the tremendous success of these missionaries. One may wonder whether the passage is referring to the missionary work of just Aaron and his brethren or whether Ammon should be included. By the time we get to Alma 23:9, the text makes it clear that Ammon’s converts are also being included:
In other words, the listing of converts here includes Ammon’s converts in the land of Ishmael (who were under king Lamoni’s rule). The entire listing (covering verses 9–12) is therefore consistent with the corrected reading earlier in verse 6, “Ammon and his brethren”.
Thus the narrative supports the corrected reading in 𝓟 for “Ammon and his brethren”. In Alma 23:6, Oliver Cowdery initially wrote “Aaron and his brethren” in both 𝓞 and 𝓟 because this phrase had just occurred a short time earlier in Alma 23:4, but there the text properly refers to the newly permitted freedom of Aaron and his brethren to travel throughout the entire kingdom of king Lamoni’s father.
Summary: Accept in Alma 23:6 the corrected reading in 𝓟, “Ammon and his brethren”, apparently also the corrected reading in 𝓞; the narrative here moves from referring to the freedom to preach given to “Aaron and his brethren” to discussing the missionary success of “Ammon and his brethren”.