The story
From French, from an Evenki word which Peter Simon Pallas transcribes as piika or peeka, but which cannot be found in modern dictionaries. Probably ultimately onomatopoeic. Compare typologically German Pfeifhase (< pfeifen (+ Hase) << Latin pīpō), Czech pišťucha, Russian пищу́ха (piščúxa) (akin to пища́ть (piščátʹ), писк (pisk)).
Etymology from Wiktionary, CC BY-SA 4.0.