Kocchi, also known as Come-Come, is a small male kitten with distinctive black markings on his front legs and back half. A black patch covers one ear and partially obscures the eye on the left side of his face in most media, though this marking appears on the right side in the original manga. He has a sharp gaze and a short tail. His personality is initially rough, bossy, and sometimes rude, particularly when defending his territory at a park fountain. Despite this, he possesses a caring nature, especially toward Chi, whom he gradually accepts and mentors in the ways of being a cat. Other characters, like Blackie, describe him as a hard worker, and he shows a playful side with friends.

Kocchi's background involves early hardship; he and his siblings lived in a box in a park until humans took his siblings away, leaving him alone. He never saw them again, deepening his loss. He formed a bond with his brother White-White, promising to wait for him after children took White-White. This promise anchored Kocchi to the park, where he established his territory and first encountered Chi. Their initial relationship was strained, as Kocchi viewed Chi as a nuisance, but they grew close through shared adventures, such as searching for food or navigating dangers like sleeping on a road where they nearly got run over. The Yamada family temporarily took him in after this incident, but he returned to the park, unable to adjust to indoor life.

Kocchi's development intensifies later when he learns from Ann about a sighting of a white kitten resembling White-White. This prompts him to leave the park on a journey to find his brother. His search leads him to a town where he reunites with White-White but observes his brother content in a new home. Overwhelmed by mixed emotions, Kocchi flees and encounters Diplo, a traveling cat, who becomes his companion. Together, they face challenges like climbing mountains and meeting other nomadic cats. During his travels, Kocchi stays briefly with a university student named Mami, who provides care and affection, allowing him to open up emotionally. However, after dreaming of White-White and reflecting on his bonds with Chi and his park friends, he realizes where he truly belongs and decides to return, prioritizing his found family.

His relationships include a protective dynamic with White-White, a mentorship-turned-friendship with Chi, mutual respect with Blackie, viewing Diplo as "weird but cool," and friendships with Terry and Ann. An OVA special details his first meeting with Chi. In one episode, a woman in an alley feeds him and calls him "Tiny," an alias reflecting his vulnerability. The name "Kocchi" itself means "come here" in Japanese, stemming from a woman at a "Good Place" urging him to approach.