It is very difficult to determine how the original manuscript read for this name. The 1830 edition has Joneam. In the printer’s manuscript, scribe 2 initially wrote Jeneum, but later (in somewhat heavier ink flow) he corrected the first and second vowels. The problem is that it is difficult to determine which vowels they were corrected to—or even whether there was a change! The 1908 RLDS edition, following one possible reading of 𝓟, changed the name to Jeneum. This same interpretation was adopted for the 1981 LDS edition, perhaps under the assumption that the 1830 reading was derived from the printer’s manuscript (which is not the case here in Mormon).
Let us consider in turn each of the three vowels for this name. For the first vowel, scribe 2 of 𝓟 definitely wrote an e initially (there is a loop there), which he later corrected by adding an additional stroke. This corrected vowel could be read as an e or as an o. In my discussion under Mormon 4:20 regarding the name Boaz, I noted that when scribe 2’s e looked like a dotless i, he would often rewrite it as an e by adding an additional stroke. Here in Mormon 6:14, however, the first vowel is definitely an e, so his altering of the vowel seems to indicate a change to o. This change would therefore make the corrected first vowel read the same as the o vowel found in the 1830 edition. As noted under Mormon 2:4 regarding the name Angolah, Oliver Cowdery frequently produced o’s that looked like e’s. Apparently, here in Mormon 6:14, his o vowel in 𝓞 looked somewhat like an e, which led scribe 2 of 𝓟 to initially write the first vowel as e but then reinterpret his decision and correct the e to an o.
For the second vowel, scribe 2 intended to write an e but actually wrote a dotless i, which he then corrected to an e by adding an additional stroke. As noted already under Mormon 4:20, this kind of correction is found elsewhere in Mormon. Since the 1830 edition also has e, we can be fairly confident that the second vowel was an e in the original manuscript.
For the third vowel, we have u in the printer’s manuscript but an a in the 1830 edition. This variation reminds us, of course, of the u-a variation discussed under Mormon 6:2 regarding the name Cumorah. Based on the discussion there, the odds are that the original manuscript had a u rather than an a, although the u probably looked like an a.
Internal evidence from other names and words in the Book of Mormon provides some support for Joneum, although not a lot. First of all, there is a name that begins with Jon, namely, Jonas (listed twice in 3 Nephi 19:4); but there are no other names that begin with Jen. In addition, when we consider Book of Mormon names and words that end in eum, there are two examples, Neum and sheum, but there are none ending in eam.
Thus both internal and external evidence, although not overwhelmingly, supports the spelling Joneum, the corrected spelling in the printer’s manuscript (it would appear). This reading for the name is only one vowel difference away from the 1830 reading, Joneam.
Summary: Change in Mormon 6:14 the spelling of Jeneum to Joneum, the corrected reading (it would appear) in 𝓟 for this name; the evidence for this correction is largely supported by patterns of scribal errors and corrections, although there is some minor support from the form of other Book of Mormon names and words.