How to quickly find the fully qualified name of a class

Press Ctrl+Alt+Shift+C (Edit | Copy Reference) on "Editor" in the code and you'll have the fully-qualified name in your clipboard.

Or alternatively just right-click on the code and select "Copy Reference".

Ctrl and hover (or ⌘ and hover)

If I hold Ctrl and hover over the class name Element with my mouse, I get a popup with the following information (assuming Element extends AbstractElement and implements IElement):

[intellij-module-name] com.whatever
public class Element extends AbstractElement
implements IElement

The package name after the module name on the first line, plus the name of the class itself, would give you the fully-qualified name in your head. You can also Ctrl+Left Click on the Element class name to jump to its definition, where you could copy out the package declaration from the file if you need the actual text in the editor for whatever reason.

For macOS, hold ⌘ while hovering mouse pointer.

Pressing Ctrl+Q when the cursor is inside the class name, will show you the class's package name and the Javadoc for that class. Esc will then close the window.