In the printer’s manuscript, Oliver Cowdery initially wrote Kumenonku, which he first corrected to Kumenonhi. But then he changed the spelling once more, this time to Kumenonki by overwriting the h with a k. The 1830 compositor set Kumenonhi.
The problem here seems to have been that in the manuscripts Oliver Cowdery’s h sometimes looked like a k (and vice versa). This problem has already been noted in the discussion under 1 Nephi 19:10 regarding the spelling of the name Zenoch /Zenock. For instance, in Helaman 8:20 of 𝓟, Oliver apparently intended to write Zenock, but his k could be read as either a k or an h. The 1830 compositor interpreted the k as an h and set Zenoch there.
It is possible, then, that the same thing occurred here in 3 Nephi 19:4—that is, the original manuscript read Kumenonki, but the k looked like an h. In other words, Oliver Cowdery and the 1830 compositor were both confused, but Oliver ultimately corrected the text to read Kumenonki. Yet it is equally possible that the intended spelling in 𝓞 was Kumenonhi, but since the h looked like a k, Oliver became confused as he was copying from 𝓞 into 𝓟.
Given this ambiguity, it is probably best to let internal evidence from the spelling of other Book of Mormon names and Nephite words determine whether we have Kumenonhi or Kumenonki. Elsewhere, we get the following sequences of a nasal followed by a voiceless obstruent (that is, a noise-like consonant without voicing); for each sequence I list all the examples except in the case of nt (which has numerous examples):
nc Moriancumer, Ripliancum, Teancum
mh Limhah, Limher, Limhi
nt antion, Antipus, Coriantumr, Gaddianton, Irreantum, Lehonti, Morionton, onti, Seantum, etc.
Historically, the p in Rameumptom may be considered intrusive, just as it is in the spelling of the English name Thompson (from Thom + son). In any event, there are no examples of nk (or mk ) in Book of Mormon names or Nephite words. But a nasal (m or n) can definitely be followed by an h sound. Thus internal evidence argues that the 1830 spelling Kumenonhi is more consistent with other spellings in the Book of Mormon and should therefore be retained. A name like Kumenonki runs contrary to all the other Book of Mormon names and words.
Summary: Accept in 3 Nephi 19:4 the 1830 reading Kumenonhi since the form Kumenonki (the final reading in 𝓟) has the sequence nk , which is uncharacteristic of Book of Mormon names and words.