What is the name of Woody's horse in "Toy Story 2"?

Woody’s horse in Toy Story 2 is named Bullseye.

Bullseye is introduced as part of the fictional Woody’s Roundup collection, a group of toys based on a popular 1950s-style Western television show. When Woody is taken to collector Al McWhiggin’s apartment, he meets Bullseye alongside Jessie the Cowgirl and Stinky Pete the Prospector. The discovery helps Woody understand that he is part of a larger, valuable collection.

Unlike Woody and Jessie, Bullseye does not speak using human language. He communicates through expressive body language, whinnies, and other horse-like sounds. Even without dialogue, his loyalty and emotional reactions are central to the story. He becomes distressed when Woody considers leaving the Roundup Gang behind and returning to Andy.

Bullseye is sometimes described as Woody and Jessie’s horse, although he is specifically a toy horse and a character within the fictional television series. He later appears in Toy Story 3, Toy Story 4, and several Toy Story short films. His name is a Western-style reference to the target symbol often associated with accuracy and marksmanship.