Hi! kudrat. Thanks for the details.
OneNote Online reads notebook metadata from the OneDrive sync service, not directly from the OneDrive file system. Renames and deletions propagate through Microsoft Graph sync queues, which can be delayed several hours depending on load. If you want the change to show instantly, clear OneNote cache or sign out/in again on the web and force refresh OneNote Online by opening it from the renamed folder link directly in OneDrive.
And about deleting unwanted notebooks, you cannot directly delete a notebook from within OneNote because OneNote doesn’t “own” the storage, OneDrive does. Closing a notebook in OneNote only removes it from your app list, it doesn’t delete the files. That's the reason why you don’t see a delete option inside OneNote.
Best regards,
Kimberly