Actually Nagesh is describing it correctly and his example is a good example. It does not matter if the sent header is called "Authorization" or (like in your case) X-SUP-DOMAIN
Your last configuration screenshot should be fine:
ClientHTTPValues To Send
--> Name of the http header which should get forwarded from SMP to configured HTTP/HTTP authentication Server. In your case: X-SUP-DOMAIN.
When you send the request to SMP you must include this header, otherwise authentication will be failing
Send Client Http Values As
--> Here you can define in what header (or cookie) SMP should forward the value of the header that got defined in previous field (ClientHTTPValues to Send). Because your auth server is awating header X-SUP-DOMAIN you should use header:X-SUP-DOMAIN
Usually you do not know the value of a header, that is why you do not need to specify the value here (BCA...), the value get forwarded based on the key (header name).
Regards
Marvin