Just click on rename and type alt + 0160 (on the numeric keypad) it will make a invisible character

Note:  This will only work if you have the file extensions hidden.

You can use this only for one icon of each type (shortcut, folder, exe, txt, jpg or whatever you have on your desktop)
For the second icon type: alt+0160 alt+0160
For the third type:  alt+0160 alt+0160 alt+0160
......