I think I found a solution for changing the SSL (Moving from HTTP to HTTPS).
- Go to the Web Map that reads from that map service or the feature service.
- Edit the Web Map then Go to the Setting tab.
- Scroll down till you see the "Layer Settings" section.
- There is a button "Update Layers to HTTPS" click on it and I will update your layers to use the HTTPs!
The result:
The location of this button is weird, it should be inside all feature layers or map services not only in the web map!
I will leave this question open because this method doesn't provide a solution in the case of the service name change or the domain name change.
-Ahmad