On a fresh install of EE (7.3.14) , if you simply Change the "Short name" in the "Settings" tab, it will create the new templates directory in "users/templates/" and it will duplicate the contents of "default_site" to it.
Process I used:

• Set up the fresh install
• In "Settings" I kept the "default_site" short name
• Went to "Templates" and created a "site" template group and set it to the default template group and put "Template 1" in the index.html file
• Went back to "Settings" and changed the short name to "IncentivEZE" and when I look in my file system, I see the new templates directory alongside the old one. If I change the contents of the site/index.html file in that new one to IncentivEZE I can see that I am able to switch between those 2 at will by changing the short name in Settings.