Both harmonica and harp are borrowed names, and neither one is the only correct name. The harmonica was invented during the Romantic era of Beethoven and Schubert, a time when garden décor included the Aeolian harp, a stringed harp that you set outdoors, where the wind makes the strings vibrate. Even though the harmonica has reeds sounded by a player's breath instead of strings sounded by the wind, some early harmonica makers referred to their instruments as Aeolian harps by way of poetic association.
Early harmonica makers in German-speaking countries used the term mundharfe (mouth harp). Still others called it mundharmonika (mouth harmonica), borrowing the name of the glass harmonica, which is played with a moistened fingertip rubbed on the rim of a glass. Meanwhile, American books were comparing the harmonica to a harp as early as 1830, and the introduction of a model called the French Harp in the 1880s may have helped to popularize calling it a harp in the American South.