From Middle Chinese compound 天鵞(then nga, “swan”, literally “heavenly + goose”). The second character 鵞 has apparently been superseded in modern Chinese by the alternative form 鵝. Compare modern Cantonese天鵝(tin1 ngo4).
This word appears in the 1734 work 本朝世事綺談 (Honchō Seji Kidan, “Embellished Tales of Everyday Japan”; also listed as 本朝世事談綺, with the last two characters swapped), in a description of the kanji spelling of 天鵞絨(tengajū, alternative reading birōdo, “velvet”, archaic, largely replaced by the borrowed term ビロード(birōdo)).