Does the restaurant "Bubba Gump Shrimp" have a link with the movie "Forrest Gump"?

Yes, the Bubba Gump Shrimp Co. seafood restaurant chain was inspired by the movie "Forrest Gump"!

Benjamin (Bubba) Bufford-Blue, Forrest's late best friend in the military and great shrimp specialist, dreamed of starting his own shrimp fishery and kitchen business - under a brand that would bear his name. Forrest keeps his promise to his friend by becoming captain of a shrimp trader under the company name "Bubba Gump Shrimp".

Each restaurant also has a souvenir shop!

The first "real" restaurant for the Bubba Gump Shrimp Company chain opened in 1996 in Monterey, California. It is to date the only existing restaurant chain based on the exploitation of a film license.