1

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.

2

What's its name?

As far as its name goes it's called the "Application Menu".

   ss #1

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.

                             ss of appmenu

NOTE: A critical step with this particular extension, you must restart gnome-shell after installing it.

Typing 'r' or 'restart' in the Alt+F2 prompt will restart GNOME Shell. This is useful when you are make changes to the GNOME Shell code while working within the GNOME Shell. You don't need to compile anything if you only changed JavaScript code, but you need to run compilation as you would normally do for C code before restarting.

Source: Developer tools GNOME3 Cheatsheet

After enabling this plugin via the GNOME3 extensions website and restarting the gnome-shell it worked fine.

      ss #2

  • I tried both without success. Extension hides activities part: imgur.com/UyvNUWY.png editing shell conf: imgur.com/6staYQs.png – user170534 Mar 2 '14 at 12:05
  • @user170534 - Try restarting gnome-shell afterwards, this enables this extension, I'll add that important detail to my A as well. – slm Mar 3 '14 at 0:47

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