The long form of "KTM" is "Kronreif, Trunkenpolz, Mattighofen." This refers to the full name of the Austrian company that manufactures KTM motorcycles. The company was founded in 1934 by engineer Hans Trunkenpolz in Mattighofen, Austria.
"Duke" is the model name used by KTM for its line of street motorcycles. The term "Duke" does not have a specific long form.