The visible page is not the whole PDF. Every PDF carries a metadata dictionary that records the document title, author, subject, keywords, the application that created it, and the dates it was created and modified. None of that shows on the page, and most of it survives ordinary exports.
The leak that matters
The author field is the one that gets people in trouble. A motion prepared on a laptop whose OS login is the case name, or by a firm whose PDF tool fills in the attorney name, ships that name to the opposing party — visible to anyone who opens the file properties. Custom fields are worse: some tools write the matter number or client ID into the /Info dictionary, where no one sees it until the recipient opens the document info and the whole case is on screen.
Embedded files are the extreme case. A PDF can carry an attachment inside it, and attachments survive every export that only touches page content. If the file contains an internal memo, it goes out inside the PDF.
What to do
Strip metadata before producing. A production tool should offer it as part of the output step, and a verification pass should tell you when the author, a custom key, dates, an XMP packet, or an embedded file is present — before you send, not after.
Not legal advice. Whether a numbering scheme or a production practice satisfies your court, protective order, or production agreement is yours to confirm.