How can I change the file private URL So I've uploaded a private file. It can be accessed like following:

http://drupal8.dev/system/files/2016-12/README.txt

How can I change how that file is accessed?

http://drupal8.dev/files/README.txt, etc.
Assuming I understand the question: To the best of my knowledge, you cannot. For a file in the private file system, the file URL must be rendered on a page in order to be accessed. Redirects and rewrites won't work.