A "Very Small Animal" Named Piglet
The first of the Disney adaptations of Winnie-the-Pooh appeared in 1966. Piglet was absent, replaced by Gopher, which, according to director Wolfgang Reitherman, was believed to have a "folksy, all-American, grass-roots image." After protests by fans, Piglet was reintroduced in 1968's Winnie the Pooh and the Blustery Day. Disney still makes film and television programs with Pooh and Piglet, most recently Piglet's Big Movie (2003). There is a lot of Piglet merchandise out there, unsurprisingly. You can get a sense of the ongoing legal battle between the Milne family and Disney from a BBC article here.
Speaking of children's toys, I still have my childhood Steiff bear, identical to the growler model that the real Christopher Robin Milne had (see picture; Piglet is the very small animal in the middle, to the left of the stack of books). I too called my bear Pooh, although it hasn't survived in nearly as nice shape as Milne's. You can see the original toys at the New York Public Library, by the way. I must have seen the Disney films in the late 1960s, but I've largely forgotten them. I certainly prefer the original look of Ernest Shepard's Piglet and his friends.