If you have Raspbian, it comes with LXDE installed and configured. With other distributions the situation is similar: The choice of a desktop environment is so much a defining feature of the distribution that if you decided to go with the distribution, you will know what is the default DE.
If you install another DE and start to use it, you'll know what you installed and started to use.
You can check what processes are running on the computer and read about those programs - some will be associated with a specific DE.
When using Ubuntu, and changing the DE to something else from the default Unity, there is a program called a display manager to manage different 'sessions'. If you have installed several DEs, you can log out from your session, and choose a different session with a different DE from the display manager. The name of the session reveal the DE.
Looking at the desktop you could e.g. check what is in the start menu and if there is some 'about', 'info' or 'help' option there. You'll find enough information that way to identify your DE. My desktop computer's start menu has a mouse icon telling me quite enough. If I right click on the panel, there is info to be found about the panel. My panel is 'xfce4-panel 4.11.0'. That tells me enough.
If your desktop is a real mix of different programs from different DEs, it could be that the question - of what DE is in use - could be more of a practice in semantics than a real question.