A tool like gconf-editor is great for adding or removing some default icons on your desktop. We can add the trash can as well as remove the home folder or Computer icon.
Before - Default Desktop Icons: (Indudes Computer and Home Foler)

Open a terminal window
Menu > Terminal


Type the following command
gconf-editor

You should now see a window similar to the image below.

Click on Apps

Scroll down and click on nautilus

Select Desktop

On the right hand side you should see some options to show icons such as computer, network, home folder, and the trash icon. Uncheck the ones you wish to hide.
The changes should be in real time so as you uncheck or check an item you will notice the icon appear or disappear.

Now just close out gconf-editor and start enjoying your changes.
After: Edited Desktop Icons - Removed Computer and Home folder and added Trash Icon

If you enjoyed this post, please share it on your favorite social network by clicking on the “Share / Save” bar below.