Duke comes from the Latin word dux (leader). It's related to the verb dūcere (to lead; pull), whence English -duce, for example in to seduce (whose original Latin meaning was 'to lead astray').
The second part of German Herzog (duke) is cognate to dux. This part, -zog, is related to the German verb ziehen (to pull), cognate of dūcere.
Old English had cognates of both words. Its counterpart of Herzog was heretoga (army leader). In Middle English it became heretowe, which would've become modern *hartow. The Old English cognate of ziehen was tēon. This verb would've become *to tee if it had continued to exist. See the infographic for information about its past tense and past participle.
Umberto Brunelleschi, Fashion illustration, Toilette au goût Vénitien (Venetian Costume), Costumes Parisiens, Journal des dames et des modes, 1913.
Illustration with a design for a "Venetian Outfit", part of the 54th issue of the "Journal des dames et des modes", published in Paris on November 20, 1913. The illustration features a woman wearing a pink jacket with wide hips, decorated with bundles of purple and white flowers, and with white fur borders and pleated sleeves over a yellow blouse with similar floral patterns and gold borders, and a pink, draped, ankle-length, narrow skirt. She wears a Navy style black hat on her head, with a large, black lace veil hanging from it over her shoulders and back, a necklace with a large, round green stone, and lavender shoes with small, golden buckles. (x)