Ubuntu 18.04 Remove Trash Icon from Desktop

First find the Trash related settings with gsettings command.

boby@ok-pc-01:~$ gsettings  list-recursively | grep -i trash
org.gnome.gedit.plugins.filebrowser.nautilus confirm-trash true
org.gnome.desktop.privacy remove-old-trash-files false
org.gnome.eog.ui disable-trash-confirmation false
org.gnome.nautilus.preferences confirm-trash true
org.gnome.nautilus.preferences show-move-to-trash-shortcut-changed-dialog true
org.gnome.DejaDup exclude-list ['$TRASH', '$DOWNLOAD']
org.gnome.nautilus.desktop trash-icon-name 'Trash'
org.gnome.nautilus.desktop trash-icon-visible true
boby@ok-pc-01:~$

To disable the Trash Icon on desktop, run

gsettings set org.gnome.nautilus.desktop trash-icon-visible false

Method 2

If you have gnome tweaks tool installed, go to Desktop, you have option to disable Trash Icon.

See Ubuntu 18.04