1. The "trace" of an orthogonal projection of a vertex of a triangle "down" to the base is called height of the triangle. (Compare Altitude (triangle) - Wikipedia, the free encyclopedia).
2. The orthocenter is the intersection of these "traces" as you've stated correctly.
3. If you use the meaning of the word: ortho means right, gonos means vertex, so "orthogonal" means "of a right angled vertex".