If you are broadcasting your SlingStudio project to Facebook Live using the Facebook support that is built-in to SlingStudio Console, then Published by SlingStudio is always displayed. But it's displayed only to you as an "admin" for the account. No one else can see it.
If you want to confirm this, look at the public view of the stream. You'll see that Published by SlingStudio is not shown.
We are not aware of a way to prevent Published by SlingStudio from being displayed to admins if you are using the Facebook Live streaming feature with SlingStudio Console (which uses native Facebook APIs).
You might be able to do this by creating a custom RTMP setup within SlingStudio Console, and then stream to Facebook that way.