Media Title appearing in View when HTML is stripped
This ended up being a media field label and not the media type name, like I originally thought it to be.

This was happening due to the media label being set to "Visually Hidden" instead of "Hidden"

This setting can be found at
Administration > Structure > Media types > [your media type] > Manage Display 

Now that it's set to "Hidden" it no longer shows in the label in the view or the WYSIWYG