Redaction that actually removes the text
A black rectangle drawn over a name is a picture of a black rectangle. The name is still in the file, and it is still selectable.
Why does a black box not work?
Because a PDF stores drawing instructions rather than a picture of a page. Adding a black rectangle adds one more instruction on top; the instruction that draws the name underneath is untouched, so selecting the area still copies the name and any search still finds it.
This has produced most of the well-known redaction failures in published documents. The file looked correct in a viewer, and the text came straight back out with a copy and a paste.
What does a real redaction do?
It deletes the content and then covers the space. The text objects, image data and annotations inside the marked area are removed from the file, and only then is a filled rectangle drawn where they used to be. What is left has nothing underneath it to recover.
Deleted is the word that matters. After a real redaction the document is a different document: search finds nothing, extraction returns nothing, and the bytes that held the name are gone rather than hidden.
How do I check that it worked?
Extract the text from the finished file and read it. If the name you redacted is still in the output, the redaction painted over it rather than removing it, and no amount of looking at the page would have shown you that.
Run the check on the file you are about to send rather than on a preview. Redacting and then saving through another tool can bring the original back if that tool works from an earlier revision of the document.
What else leaks besides the page?
The metadata and the document’s history. Author names, the software that produced the file, creation and modification timestamps, and sometimes the full path of the folder it was saved from all sit outside the pages and survive any amount of redacting.
Attachments and form field values sit outside the page content too. A document that has been through several rounds of editing may also hold earlier versions of its own objects, which is why anything destined for publication is worth rewriting from scratch once the redaction is done.
Where to go from here
Redact PDF removes the marked content and then covers it, removing the metadata handles everything outside the pages, and flattening turns annotations and form values into fixed content so nothing is left interactive.
Removing a password you own covers the difference between hiding and protecting, and PDF privacy on the web explains why none of this involves sending the document anywhere.