Short answer
On a Mac you can merge PDFs in Preview (open one, show thumbnails, then drag other PDFs into the sidebar and re-save) — or use this browser tool to combine several PDFs in a chosen order without opening an app. Everything runs locally, so nothing is uploaded.
Preview's thumbnail drag is handy for two files, but it gets fiddly with many, and it's easy to accidentally insert pages in the wrong place. This tool joins any number of PDFs in the exact order you add them and gives you one clean combined file.
Because the merge happens in your browser, confidential PDFs — contracts, statements, medical forms — never leave your Mac.
Use Preview — open a PDF, show the thumbnail sidebar, drag other PDFs in, then File → Export as PDF. This browser tool is a faster alternative for combining many files in a set order.
No — the merge runs entirely in your browser, so your PDFs stay on your Mac.