I am trying do perform a displacement map in a conical shape. I created a circle, extruded in Z and resized at the other side. After that, I selected everything and subdivided to have a bunch of small faces. Then, I added a displace modifier and a image texture, so that it becomes like the surface in the top (Object Mode):

The problem is, when I change to Edit Mode I can see that the normals keep as the surface was completely regular, which is not desirabe. I wanted the normals to follow the surface relief, is there a way to do that?

Edit: Accepted answer from Robin Betts, results (I extruded the surface, so that I can have normals on both sides):