In a quadrilateral, consecutive angles and opposite angles are congruent. What is the most specific name of the figure?

The four angles are congruet. So each angle is 90°.

So the figure is a rectangle. It could be a square but not necessarily. You can consider a square a special case of rectangle.

The four angles of a rectangle are congruent. And the opposite sides are congruent.

The four angles of a square are congruent. The opposite sides are congruent, furthermore the four sides are congruent.