And that means he wasn't actually the owner of Bubba Gump Shrimp. In fact, the restaurant chain didn't even exist until ~after~ the movie was released.
Paramount Pictures basically wanted to hone in on the movie's success, so they created the idea for a themed restaurant. The first Bubba Gump Shrimp Co. was opened in 1996, two years after Forrest Gump was released.