In the old days, before laptops, we used to call the case and everything in it the CPU. You had your monitor, keyboard, mouse, maybe printer, maybe modem, and they would all plug into the “CPU.” Yes, we knew there was also a chip inside called that but we didn’t get all pedantic about it.
With that in mind: Place the heat sink on the CPU fan… That’s exactly what they did.
I think those are where the name “desktop” comes from, though that term now refers to other computer things.
I refer to them as “tower”, “case” (which is technically just the shell and frame, but can include the contents), “computer”, or “machine”.