In distinguishing between Herren and Damen, I would have guessed that that Herren would be for men, because it’s similar to Herr, which is one of the few German words I know.
I know that Damen is cognate with the English word dame, from the etymology information in the German edition of Wiktionary on both the German and English words Dame.
But looking at the Wiktionary entry on Herr, it mentions a feminine gender word Herrin, meaning Lady. Is this more of a rare exception than the rule? Or is it unsafe to assume that words cognate with Herr are typically referring to men?