Drawing a black rectangle over a name is the most common way people leak the thing they were trying to hide. The rectangle is an annotation sitting on top of the page. The text underneath is still in the file, and it copies straight out. If you want the longer version, along with which editors do redaction properly, you can read more in this comparison of PDF tools.
It happens to people with lawyers
In January 2019, attorneys for Paul Manafort filed a court document with passages blacked out. Reporters selected the text, pasted it into another window and read it. The redacted material included details the filing was specifically meant to withhold.
It was not an obscure technical failure. It was a rectangle drawn over live text, which is what most people mean when they say they redacted something.
Even proper redaction can leak
Researchers at the University of Illinois studied redactions in US court filings. The glyph positions around a removal often reveal the length and shape of what was taken out. They identified more than 6,000 vulnerable redactions, and recovered hidden surnames in roughly 38% of the cases they tested.
The lesson is not that redaction is hopeless. It is that redaction is a document-wide operation, not a drawing tool.
How to do it properly
On a Mac, Preview has a real redaction tool. Select the text, redact it, and when the document closes the removal becomes permanent. The content is gone from the file rather than hidden behind a shape.
Acrobat Pro removes the content and then offers to sanitize the document, which strips metadata, hidden layers and attachments that may still hold what you deleted. Acrobat Standard does not include redaction at all, which is worth knowing before buying the cheaper tier for compliance work.
If your tool only draws shapes, do not use it for this. Export the pages as images and rebuild the document, or retype the section into a clean file. Both are clumsy and both work.
Things that hide content without removing it
Cropping a page hides the cropped area; the content is still there. Covering an image with a white box leaves the image. Changing text colour to white leaves the text. Flattening helps in some tools and not in others, so verify rather than assume.
The check that takes ten seconds
Open the finished PDF, select all, copy, and paste into a plain text editor. If anything you redacted appears, the redaction failed. Run a search for a name you removed as well, since selection can be fiddly.
Do this every time. It is the only step in this post that catches the mistake before the file leaves your machine.