You can rename, or even delete a file while it is open, on Linux, *BSD, and similar OSes. That's one way to create a temporary anonymous file, which will disappear as soon as your open handle to it closes. It is caused by the strong dissociation between file name and file contents. Hard links are another example, where you can have two independent and completely fully qualified (no limits) paths to the same file contents.

Also, if on those platforms, you attempted to rename a log file for for example Apache while it is running, you'll see it doesn't stop it from still growing.

Windows won't allow you to rename or delete the file while its open, that's true.