In Kemono Friends 3, she is often seen holding a large kine (杵/きね), a type of heavy wooden hammer that is used to pound mochigome (glutinous rice) into the chewy mochi, a Japanese rice cake.
Judging from her in-game Miracle animations, Tsukuyomi-No-Shinshi is based on the mythical figure, Moon rabbit, or Moon hare, that appears in various Asian folklores. Moon rabbit is an example of pareidolia interpretations - humans' tendency to perceive random visual stimuli as meaningful patterns. In this case people identified the dark markings on the near side of the Moon a rabbit or hare since the ancient time when little was known about the Moon.
In Chinese folklore, the rabbit, commonly called "Jade Hare" (玉兔), is often portrayed as a companion of the Moon goddess Chang'e, constantly pounding the elixir of life for her with a mortar and pestle, while some show the making of cakes or rice cakes. For the versions in Japan and Korea, the rabbit is pounding the ingredients for mochi, a type of rice cake. the Moon rabbit in the Vietnamese folklore often appears with Hằng Nga and Chú Cuội, and like the Chinese version, the Vietnamese Moon rabbit also pounding the elixir of immortality in the mortar. Certain Amerindian cultures of North America also has rabbit themes and characters in their Moon folklores unrelated to Asian ones.
This Friend is named after Tsukuyomi-no-Mikoto, the Moon god in Japanese mythology and Shinto religion. Tsukiyomi can be translated to "moon reading" while Shinshi can mean "messenger from the god'. In one story, Amaterasu (天照大神), the goddess of the Sun, was searching for a suitable spot for a temporary palace. A white hare appeared and held Amaterasu's clothes in its mouth to guide her to a plain, which is now called "Ise ga Naru" (伊勢ヶ平), on the peak of Reisekizan (霊石山) located in present day's Kawaharacho Inatsune, Tottori, Japan. The white hare was in fact the deity of Tsukuyomi-no-Mikoto, which was later called Dōso Hakuto Daimyōjin (道祖白兎大明神). There is no record, however, that this hare is called Tsukuyomi-No-Shinshi.
During the "高まれ！ 月光の夜想曲！！" event story in Kemono Friends 3, Yatagarasu is reminded of Tsukuyomi-No-Shinshi and the name 'Jade Rabbit' (ギョクト/玉兎) is slipped out but she immediately corrected herself by saying Tsukuyomi-No-Shinshi is better suited name.