Wikipedia tells us it's the name of a German physicist, musician and instrument maker: Ernst Florens Friedrich Chladni (1756-1827).
You're right in assuming that the spelling of his surname is untypical of German. His parents, Wikipedia reveals, came from Slovakia; Ernst, however, was born in Wittenberg, Germany. I would have pronounced the surname as /xladni/, but Wikipedia offers the 'germanised' pronunciation /ˈkladnɪ/.
Anyway, he conducted some research on vibrating plates thereby inventing a method for visualising the vibration patterns of sounds (see pictures 2 and 3):
|picture no. 2|
|credit: The Whipple Museum|
|credit: The Whipple Library|
|credit: European Cultural Heritage Online|