I figured I could throw a couple of pennies into the conversation, because it reminded me of an excerpt from the Francestown NH history book of 1895:
"Several of the adjacent towns are dotted with mountains, but Francestown has only one elevation that can be dignified by that name, and this has been always known as "Crotched Mountain". This is the proper spelling. In a newspaper article (1870) now before me, it is called "Mount Crotchet", and a like error escaped my eye in the proof of the Hillsboro County History (1885), it was called "Crotched" Mountain undoubtedly because of its two or three forks or summits. I think that in boyhood I heard old people speak of it as the "Forked Mountain", conveying the same idea.
The term "Crotchet" is both modern and meaningless. It was called "Crotched Mountain" in the Town Records of 1785. Also in the NH Gazetteer 1817 and that of 1874, (and probably in all the others), and in all surveys and references known to me prior to 1870."
This excerpt begins near the bottom of page 486, of the book "History of Francestown, N.H. From Its Earliest Settlement April, 1758, to January 1, 1891. With a Brief Genealogical Record of All the Francestown Families", published in 1895 by Warren Robert Cochrane & George K. Wood.
Read here:
https://www.google.com/books/edition/History_of_Francestown_N_H/llGDthBQqTMC?hl=en&gbpv=1