There are many different colloquial terms for the harmonica in different languages: harmo in French, gaita in Portuguese, gob-iron in English, moothie in Scots, not to mention Mississippi saxophone and even licking stick. As Winslow says, the Swabians (Trossingen is in Swabia, S. Germany) traditionally referred to it as Mundharfle. Mund means mouth and Harfle is the diminutive form of harp, so this translates as mouth harp and was used by the makers of the instrument. I think that puts paid to the theory I’ve read in US American publications that the name “harp” came from “French harp”, a term I’ve never heard used to describe a harmonica. There are also a number of less complimentary terms, but then, the harmonica is an instrument that has always polarized listeners 
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