How do you say "cuaderno de borrador" in English?
A notebook where you scribble, take notes carelessly or hurriedly, for example, when listening to a lecture...

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I think we'd probably just say notebook, notepad or pad.

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To be specific, we could say “scratchpad”.

By the way, carpeta de borradores would be “(rough) drafts” (you don’t have to say “folder” if it's clear in context, but if you did, it would be “rough draft folder”).

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Notebook. In English, there is not a special name for it.

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It's possibly only British English, or even Australasian English, but you can also use 'Jotter'.