Miller names the person connected with a mill—most often the grain mill that turned wheat or rye into flour. In English that is straightforward occupational vocabulary; German Müller, Scottish Millar, and related Jewish occupational calques tell the same practical story in other tongues.
Mills were fixed pieces of village infrastructure, so the surname arose wherever milling mattered, not from one clan. American Miller lines may be English, German, Scots-Irish, or other, later merged under one spelling. The shared idea is work at the mill, not a nickname for a talkative relative. If your family is Miller, think waterwheel, millstone, and flour dust—not a mystery word.