The thing indicating current open application. I know there are some extensions concerning it but I'm yet to find a way to disable it, either by good ol' editing or an extension.
What's its name?
As far as its name goes it's called the "Application Menu".
The top bar includes the activities button, application menu, clock, system status area and user menu.
Source: GNOME Shell Design
Removing it from the top bar
method #1 - hiding just the icon
As far as removing it I found this AskUbuntu Q&A titled: How do I remove the application icon from the top panel? which shows how to hide the icon portion.
method #2 - hiding the icon + text
I also found this extension, titled: Remove App Menu which looks like it will remove the Application Menu on the top bar. This shows a before and after.
NOTE: A critical step with this particular extension, you must restart
gnome-shell after installing it.
After enabling this plugin via the GNOME3 extensions website and restarting the
gnome-shell it worked fine.