I was wondering about that Truthahn thing.
Hahn (per wiktionary, Google translate) means rooster. Also means tap, faucet, stopcock, presumably because a tap looks a bit like a rooster’s head. Also, nice that the same transfer exists in English in stopcock.
Also per wiktionary, Huhn means hen. The plural Hühner means chickens. Henne also means hen: this word is a regional variant. I wonder what word would be used for a single chicken of unknown sex.
These words (like the English word hen) are thought to derive from a PIE root, *kan- meaning sing. Same origin as cantata etc. All very interesting.
As a bonus, looking into this has alerted me to the fact that etymonline now has articles on the non-controversial PIE roots, with all English cognates listed.