I suggest consulting Sweetser's guide to the White Mountains, in particular, its chapter on 'Nomenclature'. After reviewing the names of the peaks in the White Mountains, his final paragraph is:
'Out of this blind maze of homely and hackneyed names must arise the significant nomenclature of the future. Why should our mountains not bear such noble names as those of Switzerland, the Alleleinhorn, the Jungfrau, the Mischabel, the Wetterhorn, Monte Rosa -- names which resound like the roll of the avalanche? ... It must necessarily be a slow process, but it has already commenced well, and by the second centennial the entire nomenclature of our New-England highlands may be reformed. The Alps of Western America are being badly treated in this regard, and surveyors and geologists are allowing their names to be attached to peaks that rival Mont Blanc. Arizona emulates Maine in its Bill Williams Mt., and the depths have been reached in Mt. Jeff. Davis.'
(I quote from the 1887 edition, but I think the same passage appears in the first, 1876, edition. I picked the copy closest to hand.)
And Arizona still hasn't really changed the name of the peak, but now they call it just 'Mount Davis'. (And, by the way, and as you may know, there's a little bump on Monadnock named Monte Rosa.)