In the original manuscript, Oliver Cowdery initially wrote the second name as Paachi. Virtually immediately he corrected the spelling to Paanchi by supralinearly inserting an n (there is no difference in the level of ink flow for the n). It seems reasonable to assume that Joseph Smith had to spell out this name even before Oliver’s initial attempt to spell this difficult name (one wonders how to even pronounce it). The spelling Paanchi is supported by a second occurrence of the name (in Helaman 1:7), although there 𝓞 is not extant.
It should be noted that at this point in 𝓞, Oliver Cowdery spelled the name Parhoron as Pahoron. Although 𝓞 is not fully extant for this particular occurrence of Parhoron, it begins with Pah; nearby extant occurrences of the name in 𝓞 are all spelled Pahoron. For a complete discussion of the original spelling, Parhoron, see under Alma 50:40.
The name Pacumeni is extant in 𝓞 for four of its five occurrences (all here in Helaman 1), and it is consistently spelled this way without variation in 𝓞 or 𝓟. Most likely, this name was also spelled out for Oliver Cowdery the first time it occurred (here in Helaman 1:3).
Summary: Maintain the spelling Paanchi, the corrected spelling in 𝓞 for Helaman 1:3 (the first occurrence of the name in the text); the name is consistently spelled Paanchi in 𝓟 (here in verse 3 as well as in verse 7).