The case doesn't matter. That setting is set as the SameSite attribute of the cookie as is by WeBWorK. The SameSite attribute works the same with the setting of "none" or "None". All values in headers (including cookies) are case insensitive.
One option that could be tried if session cookies are causing issues is to instead use session management via keys. I.e., the traditional method. Set $session_management_via = "key"; in localOverrides.conf for this.