The safest edit
moves nothing

A file that knows where everything is

Every PDF ends with a cross-reference table: a list saying object 14 begins at byte 92,318, object 15 at byte 94,002, and so on. A reader uses it to jump straight to whatever it needs. It is why a five-hundred-page PDF opens instantly instead of being read from the top.

Which makes deletion dangerous

Remove the author's name from the middle of that file and everything after it shifts backwards by the number of characters you removed. Every offset in the table is now wrong. Some readers cope by scanning the whole file and rebuilding the map. Others show an error. You will not know which until someone tells you the document you sent them will not open.

Overwrite in place instead

The alternative is not to delete anything. Find the author's name, and write spaces over the exact number of bytes it occupied. The file is the same length, every object still begins where the table says it does, and the name is gone. It is less elegant than rewriting the document, and considerably harder to get wrong.

What it cannot fix

This handles metadata. It does not handle a PDF that has been saved several times, because those files keep their earlier versions in the body rather than in the metadata, and removing them means genuinely rewriting the document. A file like that can hide text you deleted years ago. You can spot it yourself: the marker that ends a PDF, %%EOF, appears more than once. The honest fix is to open the document and print it to a new PDF, which flattens the history away.

Why a tool should say so

It would be easy to strip the metadata, say “cleaned”, and let someone send a document that still contains its own drafts. The checker on this site reports incremental saves as a separate finding and tells you cleaning will not remove them. A tool that names its limits is more useful than one that claims completeness.