In a terminal or console, you can run:
pgrep -l "gnome|kde|mate|cinnamon"
pgrep -l "gnome|kde|mate|cinnamon"
or
ps -A | egrep -i "gnome|kde|mate|cinnamon"
ps -A | egrep -i "gnome|kde|mate|cinnamon"
The item that appears in more lines should be the answer.