Even before he obtained the plates, Joseph knew the name of the hill was Cumorah because Moroni told him. We know this from Joseph's mother, Lucy Mack Smith.
When he went on his mission to the Lamanites with Parley P. Pratt, Oliver Cowdery explained to people that Moroni said the hill was called Cumorah anciently.
Pratt wrote this hymn that memorializes what Moroni told Joseph Smith that first night--years before Joseph obtained the plates.
Oliver Cowdery wrote the most detailed account of Moroni's visit, now found in Letter IV, which you can read in Joseph Smith's personal history, here.
During his first visit to Joseph, Moroni explained that the history was "written and deposited not far from" Joseph's home; i.e., Mormon and Moroni abridged the records while living in western New York.
This was well understood during Joseph's lifetime. For example, Heber C. Kimball joined the Church with Brigham Young when they lived in western New York. (Kimball was later one of Brigham Young's counselors in the First Presidency.) Kimball wrote,
"In the towns of Boomfield, Victor, Manchester, and in the regions round about, there were hills upon the tops of which were entrenchments and fortifications, and in them were human bones, axes, tomahawks, points of arrows, beads and pipes, which were frequently found; and it was a common occurrence in the country to plow up axes, which I have done many times myself. I have visited the fortifications on the tops of these hills frequently... The hill Cumorah is a high hill for that country and had the appearance of a fortification or entrenchment around it. In the State of New York, probably there are hundreds of these fortifications which are now visible, and I have seen them in many other parts of the United States." Life of Heber C. Kimball, p. 25.
Our M2C scholars teach that President Kimball didn't know what he was talking about.
Ask your Seminary or Institute or BYU or Sunday School teacher about President Kimball's statement. Most likely, they have never heard what President Kimball wrote. They'll consult the "experts" and come back to tell you President Kimball was mistaken, or speculating, or ignorant, solely because of M2C.
It's all very simple. The prophets have consistently and persistently reaffirmed this basic teaching that the hill Cumorah of Mormon 6:6 is in western New York.
Nevertheless, the M2C intellectuals (who, unfortunately, are very influential) have persuaded many members of the Church to disbelieve the prophets.
At least we have this hymn to remind us of what really happened.
Photos of the hill Cumorah from Church history are available here:
Account of the acquisition of Cumorah here:
The Tabernacle Choir recorded the hymn here: