And this quick tutorial is going to show you how to do it in the default Ubuntu 17.10 (Gnome) desktop.
1. Open Ubuntu Software app, search for and install Gnome Tweaks, a simple graphical tool for configuring Gnome 3 Desktop.
2. Then launch Gnome Tweaks, navigate to ‘Desktop’ in left pane.
There either turn off the switch for ‘Show icons’ to hide all desktop icons, or only switch off the ‘Trash’ icon.
That’s it. Enjoy!