Even before Joseph Smith received the Gold Record from the Hill Cumorah, the family members already knew the place was called Cumorah. The only thing that makes sense is that the Angel must have called it Cumorah.
This following excerpt comes from the book Biographical Sketches of Joseph Smith the Prophet and His Progenitors for Many Generations written by the mother of Joseph Smith – Lucy Mack Smith. It is found on page 93 and you can view it here – https://contentdm.lib.byu.edu/digital/collection/NCMP1820-1846/id/16433. The book was later renamed The History of Joseph Smith by His Mother, and in my hardcopy finds the story on pages 103-104.
This chapter includes the time where Joseph Smith was chastised by the angel for not being engaged enough in the work of the Lord. Read the important excerpt below:
Not long subsequent to his return, my husband had occasion to send him to Manchester, on business. As he set off early in the day, we expected him home at most by six o’clock in the evening, but when six o’clock came, he did not arrive. We always had a peculiar anxiety about him whenever he was absent, for it seemed as though something was always taking place to jeopardize his life. But to return. He did not get home till the night was far spent. On coming in, he threw himself into a chair, apparently much exhausted. My husband did not observe his appearance, and immediately exclaimed, “Joseph, why are you so late? has anything happened to you? We have been much distressed about you these three hours.” As Joseph made no answer, he continued his interrogations, until, finally, I said, “Now, father, let him rest a moment–don’t trouble him now–you see he is home safe, and he is very tired, so pray wait a little.”
The fact was, I had learned to be a little cautious about matters with regard to Joseph, for I was accustomed to see him look as he did on that occasion, and I could not easily mistake the cause thereof.
Presently he smiled, and said in a calm tone, “I have taken the severest chastisement that I have ever had in my life.”
My husband, supposing that it was from some of the neighbours, was quite angry, and observed, “I would like to know what business anybody has to find fault with you!”
“Stop, father, stop,” said Joseph, “it was the angel of the Lord: as I passed by the hill of Cumorah, where the plates are, the angel met me, and said that I had not been engaged enough in the work of the Lord; that the time had come for the Record to be brought forth; and that I must be up and doing, and set myself about the things which God had commanded me to do. But, father, give yourself no uneasiness concerning the reprimand which I have received, for I now know the course that I am to pursue, so all will be well.”
It was also made known to him, at this interview, that he should make another effort to obtain the plates, on the twenty-second of the following Sept., but this he did not mention to us at that time.Lucy Mack Smith – Mother of Joseph Smith