I think it's not a straightforward yes or no. In the Toy Story universe, it's a bit complex and might not have a definite intended owner for Jessie like that.
Well, it's not explicitly stated that Emily was the sole intended owner of Jessie. The story leaves some room for interpretation and different perspectives on ownership.
In Toy Story, the concept of ownership for Jessie isn't clearly defined to be solely centered around Emily. There are multiple factors and storylines at play that make it not that simple to determine.
Jessie's original owner was Emily. She outgrew Jessie and gave her away.
Yes, Jessie is in Toy Story 1. She's one of the memorable characters in the movie.
Jessie is an important character in Toy Story. She's a toy with a lot of energy and enthusiasm. She has a backstory about being abandoned and then finding a new family with the other toys.
Jessie is estimated to be around 17 years old. She was made in the 1950s and her character's age is kind of implied based on that.
The voice of Jessie in Toy Story is Joan Cusack.
The voice of Jessie in Toy Story 3 is Joan Cusack.
The voice of Jessie in Toy Story 2 is Joan Cusack.