Kamuy is an Ainu word for a supernatural, spiritual being. It was believed that Kamuy would come to the human world from Kamuy Mosir and roam in the form of bears. Ainu would kill bears through the practice of iomante to free a Kamuy from its bear form and return it to Kamuy Mosir.
Design
In the Persona 4 design materials, Soejima talks about Kamui being based on Kim-un-Kamuy, the Ainu's bear god, and the bear element being why Kamui has claws. He expresses his confusion over how their traditions of worshipping bears also involve killing bears. Regardless, he designed the rocket on Kamui's back to symbolize a hunter's arrow killing a bear.[1][2] The tradition Soejima is referring to is the Ainu ritual of iomante in which a hunter would kill a bear believed to be a Kamuy to return it to Kamuy Mosir.
In Golden, Teddie starts with Kintoki-Douji. It transfigures into Kamui upon maxing his Social Link, and can further transfigure into Kamui-Moshiri during winter.
↑"Characters: Teddie", Persona 4 Official Design Works, Atlus, Famitsu Editorial Department. Published by Famitsu (2008). Japanese. p. 80. ISBN-13: 978-4757745087.
↑"5: Setting: Protagonist Personas", Persona Club P4, Atlus, Famitsu Editorial Department. Published by Famitsu (2009). Japanese. p. 198. ISBN-13: 475774630X.