If I may add a few details....
Reading the excellent books by Ralph Lee Smith: "The Story of the Dulcimer" and especially "Appalachian Dulcimer Traditions" clearly shows that the name "dulcimer" (or "dulcimore " and other variations) was already in use for the fretted dulcimer well before (at least a century) the folk revival of the 1970s. I have a little personal hypothesis about this strange disambiguation of the two types of dulcimers :
The King James I Bible, first published in 1611, quickly became the version authorized by the Church of England. The passages that interest us are in the book of Daniel: 5, 10 and 15.:
"Now if ye be ready that at what time ye hear the sound of the cornet, flute, harp, sackbut, psaltery, and dulcimer, and all kinds of musick, ye fall down and worship the image which I have made".
In this text, "dulcimer" is used to translate the Aramaic word "sumponiah", itself derived from the Greek "symphonia" (in fact, a kind of bagpipe), which the translators did not really know what to do with at the time. It was therefore the (hammered) dulcimer, very fashionable at the time, which saved them the day, thereby making this instrument an instrument of biblical times.
In the depths of Appalaches, with practically only the Bible to read, the hardy pioneers also found themselves in the embarrassment of baptizing the youngest of the family of alpine zithers, derived from the unpronounceable Dutch "scheitholt" or "zither". It was necessary to accompany the hymns, an instrument accepted by the Church, unlike the violin (the devil's box). What's better than an instrument name quoted in the Holy Scriptures? And there you have it, the Appalachian "dulcimer".
Homonymy was not a problem for almost two hundred years, when the two instruments had well separated geographical domains. It was only after the Second World War and the folk revival and the arrival of Jean Ritchie (the damsel with a dulcimer) in New York that the need for two distinct qualifiers arose : the hammered dulcimer and the pinched/plucked/fretted/lap dulcimer...
Of course, it's nothing but a(nother) hypothesis. Sorry if I was a bit long.
In the Appalachian wilderness, pioneers baptized a new instrument, derived from alpine zithers and known as the "dulcimer." Acceptable to the Church unlike the violin, it accompanied hymns, its name found in the Bible, making it ideal for religious music in the region.