The Kindle has the concept of cdetypes, which is a metadata field describing the type of document. Examples are periodicals, ebooks, personal documents, etc.
EBOK == ebook
PDOC == personal document
Personal documents are automatically given the "Personal" banner by the Kindle firmware. By default calibre sends books as PDOCs, but there is an option in the Output preferences for MOBI/AZW3.
Set the Personal Documents tag to "EBOK" in MOBI Output, and make sure the option "Enable sharing of book content" is unchecked. That *should* do the trick.
This FAQ entry is pretty much the same thing but in reverse:
http://manual.calibre-ebook.com/faq....droid-ipad-etc
Mote that you will need to select ALL books, enter Bulk Edit Metadata (shortcut key is "E") and check "Remove stored conversion settings for the selected books" or else the previous settings take precedence.
Alternatively, you can install
[GUI Plugin] Quality Check, and use the twin options:
Check Mobi ==> Check missing EBOK cdetype
(selects all books that would be affected by this problem)
Fix ==> Fix ASIN for Kindle Fire
(inserts an ASIN which forces the Kindle to see the book as an EBOK)