In Toy Story 2, Jessie’s former owner before she is donated is named Emily.
Jessie’s memories of Emily appear during the song “When She Loved Me.” The sequence shows Emily playing with Jessie as a child, carrying her around, and treating her as a treasured companion. As Emily grows older, Jessie is left under a bed and ultimately placed in a donation box.
This history shapes Jessie’s fear that a child will eventually abandon her. It also creates an important parallel with Woody, who worries about what will happen when Andy grows up. Jessie’s experience makes her initially support Stinky Pete’s plan to send the collection to a museum.
Emily is not the same character as Bonnie, who receives Jessie and the other toys later in the series. Daisy is Lotso’s former owner in Toy Story 3, while Molly is Andy’s younger sister.