var previousOUM:String = "";
private function listObjectsUnderMouse():void {
	var point:Point = new Point(mouseX, mouseY);
	var objects:Array = stage.getObjectsUnderPoint(point);
	var currentOUM:String = ""; // Objects Under Mouse
	var results:String = "";
	for (var i:int = 0; i < objects.length; i++) 
	{
		currentOUM += DisplayObject(objects[i].parent).name
		if (i != objects.length-1) currentOUM += ", ";
	}
	if (currentOUM != previousOUM) {
		trace(currentOUM);
		previousOUM = currentOUM;
	}
}

// modified/improved version below for pure AS/Flex:


// Syntax
Application.application.stage.addEventListener(MouseEvent.CLICK, listObjectsUnderMouse);

// Variable(s)
var previousOUM:String = "";

// Function
private function listObjectsUnderMouse(e:MouseEvent):void {
  var point:Point = new Point(e.stageX,e.stageY);
  var objects:Array = Application.application.stage.getObjectsUnderPoint(point);
  var currentOUM:String = ""; // Objects Under Mouse
  var currentTypes:String = "";
  var results:String = "";
  for (var i:int = 0; i < objects.length; i++) {
    currentOUM += DisplayObject(objects[i].parent).name;
    currentTypes += DisplayObject(objects[i].parent);
    if (i != objects.length-1) {
      currentOUM += ", ";
      currentTypes += ", ";
    }
  }
  if (currentOUM != previousOUM) {
    trace("\n\n><> " + objects.length + " object(s) under mouse position (" + point.x + "/" + point.y + ").\n><> " + currentOUM + "\n><>" + currentTypes);
    previousOUM = currentOUM;
  }
}

var previousOUM:String = "";
private function listObjectsUnderMouse():void {
	var point:Point = new Point(mouseX, mouseY);
	var objects:Array = stage.getObjectsUnderPoint(point);
	var currentOUM:String = ""; // Objects Under Mouse
	var results:String = "";
	for (var i:int = 0; i < objects.length; i++) 
	{
		currentOUM += DisplayObject(objects[i].parent).name
		if (i != objects.length-1) currentOUM += ", ";
	}
	if (currentOUM != previousOUM) {
		trace(currentOUM);
		previousOUM = currentOUM;
	}
}

// modified/improved version below for pure AS/Flex:


Application.application.stage.addEventListener(MouseEvent.CLICK, listObjectsUnderMouse);

private function listObjectsUnderMouse(e:MouseEvent):void {
  var point:Point = new Point(e.stageX,e.stageY);
  var objects:Array = Application.application.stage.getObjectsUnderPoint(point);
  var currentOUM:String = ""; // Objects Under Mouse
  var currentTypes:String = "";
  var results:String = "";
  for (var i:int = 0; i < objects.length; i++) {
    currentOUM += DisplayObject(objects[i].parent).name;
    currentTypes += DisplayObject(objects[i].parent);
    if (i != objects.length-1) {
      currentOUM += ", ";
      currentTypes += ", ";
    }
  }
  if (currentOUM != previousOUM) {
    trace("\n\n><> " + objects.length + " object(s) under mouse position (" + point.x + "/" + point.y + ").\n><> " + currentOUM + "\n><>" + currentTypes);
    previousOUM = currentOUM;
  }
}

var previousOUM:String = "";
private function listObjectsUnderMouse():void {
	var point:Point = new Point(mouseX, mouseY);
	var objects:Array = stage.getObjectsUnderPoint(point);
	var currentOUM:String = ""; // Objects Under Mouse
	var results:String = "";
	for (var i:int = 0; i < objects.length; i++) 
	{
		currentOUM += DisplayObject(objects[i].parent).name
		if (i != objects.length-1) currentOUM += ", ";
	}
	if (currentOUM != previousOUM) {
		trace(currentOUM);
		previousOUM = currentOUM;
	}
}

Calling this will conditionally trace the list of object names underneath your mouse point. It will only trace when the list of objects beneath the mouse actually changes.

AS3 Get Object Names from GetObjectsUnderPoint

ActionScript 3