It is still a pencil case :)

It's a pencil case to me. It doesn't matter what it's made of, or what shape it is, the container kids put such school items in is a pencil case.

Yes, you can call it any of them. I would normally say pencil bag.

It's also called pencil case

Maybe in Latin the word meant a box, but in English, "a case" is just any sort of container specifically designed to hold an object or objects and it / them keep safe. To me, the item pictured is indeed a pencil case. Although it is more boxy than a bag, it's not really a box.