The Church has a website about Cumorah.
It's no wonder so many people are confused about Cumorah. Look at this fun quotation:
In the 1820s, the hill did not have a name. It later became known as Hill Cumorah because Moroni, the Book of Mormon’s final author and the angel who met with Joseph Smith, wrote that he had hidden the gold plates in a hill called Cumorah (see the introduction to the Book of Mormon).
Who writes this stuff? Seriously, what are we supposed to think when we read such opinion written as if it was fact.
The first statement in bold is not factual; it is merely an opinion that the documented accounts of the hill being referred to as Cumorah in the 1820s were false. This includes statements from Joseph Smith, Lucy Mack Smith, David Whitmer, Oliver Cowdery, and Martin Harris.
Of course, anyone even vaguely familiar with Church history and basic logic knows this statement cannot be shown to be true anyway. At most, we can say "we have no contemporaneous historical documents from the 1820s that identify the hill as Cumorah." But that's a far cry from saying the hill did not have a name in the 1820s, and that it became known as Hill Cumorah only "later."
Even if we didn't have statements from the people listed above, no one can say the "hill did not have a name" in the 1820s because that is proving a negative. Absence of evidence is not evidence of absence, etc. All it would take is one person giving it a name to make the statement false, and we have few documents from the 1820s that refer to the hill at all--except for recollections about events in the 1820s in which people refer to the hill as Cumorah.
The historical evidence we do have indicates the hill was "known as Cumorah" beginning in 1823 when Moroni first visited Joseph Smith. This is the most parsimonious explanation, and it explains all the other historical references.
As for the second sentence in the paragraph on the Church's website, this one is fun too because no one can point to any historical source that states or implies that the hill was named Cumorah because Moroni "wrote" that he had hidden the gold plates in a hill called Cumorah. In fact, the reason why the M2C scholars insist the "real Cumorah/Ramah" is in Mexico is because Moroni, when he wrote his portion of the text, did not identify the name of the hill where he buried the plates.
The sentence would at least be supported by historical evidence if it read, "Moroni, the Book of Mormon’s final author and the angel who met with Joseph Smith, told Joseph that he had hidden the gold plates in a hill called Cumorah," as reported by Lucy here:
the record is on a side hill on the Hill of Cumorah 3 miles from this place remove the Grass and moss and you will find a large flat stone pry that up and you will find the record under it laying on 4 pillars <of cement>— then the angel left him
Few Latter=day Saints are familiar with this historical record because it contradicts the M2C narrative. Instead, we are given nonsensical statements such as the one on the Church's website first quoted above.
As if that's not enough, the statement refers to the "Introduction to the Book of Mormon," but that reference doesn't support the claim in the second sentence either.
After Mormon completed his writings, he delivered the account to his son Moroni, who added a few words of his own and hid up the plates in the Hill Cumorah. On September 21, 1823, the same Moroni, then a glorified, resurrected being, appeared to the Prophet Joseph Smith and instructed him relative to the ancient record and its destined translation into the English language.
The historical record supports the claim that Moroni identified the hill as Cumorah when he first visited Joseph Smith, but it does not support the claim made on the Church's website that Moroni wrote that he buried the plates in a hill called Cumorah.
Everyone familiar with the historical record knows the hill was named Cumorah because
1) that's the name Moroni gave it the first time he met Joseph Smith,
2) that's the name Joseph used for it even before he got the plates,
3) that's the name used by the messenger who took the abridged plates from Harmony to Cumorah, and
4) that's the name by which Oliver Cowdery identified the hill during the mission to the Lamanites.
Plus, of course, Joseph explained in D&C 128:20 that the name of the hill preceded the time when he obtained the plates.
Readers of this blog know all these references, but the author of the sentences on the Church website apparently doesn't. The references are all available here:
Regardless of the inaccuracy of what the Church's website says about how the hill Cumorah was named, at least the maps on the Church's website accurately identify the hill as Cumorah.