I want to know the precise English word for the paper wrapped around these notebooks.
It is a bellyband:
a band of paper around a new book, usually printed with information about the book's contents and sometimes used instead of a book jacket.
a band that is used as packaging or decoration around a book, magazine, or similar item.
Apart from the formal / technical answers already posted, in everyday conversation (England, UK) I'd simply refer to it as a sleeve (or a cardboard sleeve).
a cover to protect something:
Can you put the record back in its sleeve, please?
a tube-shaped covering
(The dictionary definition says "to protect a part of a machine", but common usage would be a lot more general than that)
If you do an image search for "cardboard sleeve" in your favourite search engine you'll find a fair number of similar examples...
A paper strip wrapped around a book like a dust jacket, but smaller in height than the book. It is typically used for promotional purposes and may be added post-publication .**..
From: wrap-around band in The Oxford Companion to the Book
Subjects: Literature — Bibliography
The same would go for the notebooks in the question.
Or, less fancy, just paper bands:
I would have called this an obi (on Wiktionary as “A strip of paper looped around a book or other product”). But this is possibly just jargon relating to the paper strips included with CDs and games imported from Japan where the word originates.
wrapper noun the cover,
1)usually of paper or cellophane, in which something is wrapped
2)a dust jacket of a book
Just because the wrapper has got very small and less wasteful, that is what it is, the wrapper holding 3 books together.
And in a sentence
Just take that little wrapper off the books so we can get started.