Secure CSRF protection without sessions or database?
The method with storing the CSRF token in cookie is quite widely used (AngularJS, Django) but it works a bit differently. The server sends the token in cookie, the client uses JavaScript to read the cookie and reflect the token in a HTTP header. The server should only verify the value from the HTTP header, even though the cookie will be sent automatically as well.
The actual cookie and header names are not important as soon as both JavaScript frontend and backend are aware of them.
This prevents CSRF because only JavaScript running from the authentic origin will be able to read the cookie (see detailed discussion on Wikipedia). The token can be a HMAC of the session cookie, which avoids the need to remember token state on the server side.
The main advantage is that this approach (unlike the one with token in form fields) works with single-page, JavaScript based applications where you don't generate the HTML on the server and can't really embed the CSRF token in their code.