I'm running Ubuntu 17.10 with GNOME shell. How do I remove "Trash" icon from desktop?
You may use (GNOME) Tweaks to do that. If it is not installed, install it by
sudo apt install gnome-tweak-tool
Launch Tweaks and go to Desktop section. Then toggle off (or uncheck) the Trash (or Rubbish bin or Wastebasket) option under "Icons on Desktop".
Alternatively you may run the following command in Terminal:
gsettings set org.gnome.nautilus.desktop trash-icon-visible false