Learn English – the cover of the head of a pen called in English

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.

This is called a lining:

material that lines or that is used to line especially the inner surface of something (as a garment)^(MW)

You would ask questions such as:

What are those boots lined with?

Is the lining removable?

Do you have any gloves with fur lining?