When buying books in books-shop, we see sometimes a transparent cover which covers the book hermetically as a sign that it's new and nobody used or opened it. What is the name of this cover in English? (how to name it?) Can I say simply cover and everybody will understand What I'm talking about?
Don't confuse the clear wrapping with the dust jacket that's on a hardcover book. For most people, "cover" will mean the same thing as dust jacket.
I think what you're describing is clear plastic shrinkwrap.
A protective wrapping made from clear plastic film that is shrunk onto an object by heat
EDIT The loose plastic covering that a magazine comes in might better be called a sleeve or a mailer, since it's not shrunk tightly onto the magazine inside.
Since paper deteriorates over time, proper protection can be critical especially for older books. Many sacred texts on parchment or similar do not allow people to touch the paper as the oil from the hands can also cause deterioration to the paper. In religious circles, rarely is plastic used to protect the books, but in rare occurences when it is used, this protector is called a "Wearsie Bind"