The question here is whether to spell the name with two d ’s or only one, as Gaddianton or Gadianton. The name appears 32 times in the text but is fully extant in 𝓞 for only two instances, the second and third occurrences (later here in Helaman 2):
There is one other occurrence of this name that is extant to some degree in 𝓞, but only for the last three letters, ton (the 24th occurrence, in 3 Nephi 2:12).
For the first occurrence of the name (here in Helaman 2:4), spacing between extant fragments of 𝓞 supports the longer spelling, Gaddianton. Everything is extant on the line except for the name, so the length of the missing text is sufficiently set out that we can make a clear judgment in favor of the longer spelling. The line below lines up 14 characters (“secret work of”) with the missing name and its following space:
The spelling with the best fit is definitely Gaddianton, although one cannot be sure that 𝓞 read that way; for instance, Oliver Cowdery could have initially written Gaddianton in 𝓞 but then corrected it to Gadianton by crossing out one of the d ’s. If so, one then wonders why Oliver would have immediately forgotten the correct spelling when he came to the next two occurrences of the name, in verses 11 and 12; there he spelled the name in 𝓞 without correction or variation as Gaddianton.
In the printer’s manuscript, Oliver Cowdery consistently spelled the name with one d, as Gadianton (27 times, from Helaman 2:4 through 3 Nephi 3:15). This spelling, of course, is the reading of the current text. For that portion of the text where both the 1830 edition and 𝓟 are firsthand copies of 𝓞 (from Helaman 13 through the end of Mormon), the 1830 edition has the spelling Gadianton for the seven occurrences of the name in 3 Nephi 1–3. But for the five occurrences of the name in 4 Nephi and Mormon, the 1830 edition (as well as 𝓟, in scribe 2’s hand) has the double-d spelling, Gaddianton. This spelling argues that for 4 Nephi and Mormon, at least, 𝓞 had the double-d spelling. These five occurrences of Gaddianton in the 1830 edition were eventually replaced by the spelling Gadianton in the printed editions:
Except for the third case, it was the 1840 edition that made the change to Gadianton. The 1852 LDS edition consistently made the change in the LDS text for all five cases. The 1858 Wright edition removed the final instance of Gaddianton from the RLDS textual tradition (the third case, in Mormon 1:18).
There doesn’t seem to be any particular difficulty with Gaddianton that would have led Oliver Cowdery to change the spelling from Gaddianton to Gadianton when he copied from 𝓞 into 𝓟. Yet in the previous chapter (see under Helaman 1:9), there is definite evidence that Oliver made exactly that kind of textually unmotivated change in the spelling of a name when he copied the text from 𝓞 into 𝓟 (namely, his systematic change of Kishcumen to Kishkumen).
When we consider the spelling of other Book of Mormon names, we find examples with both the single and double-d spellings, as in the following that have a syllable or two of the form gad or gid:
For the name Gidanah, a single d in the printer’s manuscript was respelled as a double d in the 1830 edition; moreover, the second vowel, an a, was changed to an o, thus making the name identical with the Giddonah found in Alma 30:23 (see the discussion under Alma 10:2).
There are 13 occurrences in the text of the name Giddianhi, from 3 Nephi 3:9 through 3 Nephi 4:14. In two instances, the 1830 compositor set this name as Gaddianhi (in 3 Nephi 3:12 and 3 Nephi 4:9), undoubtedly under the influence of Gaddianton, especially since Giddianhi was “the governor of this the secret society of Gaddianton” (3 Nephi 3:9); perhaps there is some morphological connection between the governor’s personal name and the name of the band that he led. In the first of the two 1830 misspellings (in 3 Nephi 3:12), the 1830 compositor caught his misspelling and made an in-press correction of the spelling, from Gaddianhi to Giddianhi. This initial confusion on the part of the printer suggests that 𝓞 (which he was using to set the type for 3 Nephi 3–4) had the double-d spelling Gaddianton in this part of the text, thus facilitating the error Gaddianhi.
In general, the extant evidence from 𝓞 argues for the spelling Gaddianton; although the first occurrence is not extant, spacing in the lacuna argues for the double d. Oliver Cowdery’s systematic change to Gadianton seems to be the result of a decision on his own, but then so was his systematic change of the name Kishcumen to Kishkumen that he initiated in the previous chapter.
Summary: In accord with the two extant readings in the original manuscript, restore the spelling Gaddianton to the Book of Mormon text (32 times, beginning here in Helaman 2:4).