Oops. Ignore that last one. Wrong story. Ahem. Transformation is actually a major theme of Ovid's The Metamorphoses as a whole. The word metamorphosis actually means "to change or transform."
In the story of Echo and Narcissus, we have two major transformations: Echo becomes a bodiless voice and Narcissus becomes a flower. On the one hand, these transformations provide simple explanations for things that exist in the world. There really are echoes, and there really are daffodils. Ovid probably thought it was fun explaining where stuff came from.
But what's more interesting is that these transformations contrast the actions of the Ovid's characters. Both Echo and Narcissus fall in love, and neither of them is willing to give it up. They refuse to transform their feelings—they refuse to change. Instead, they die and their bodies do the changing. What the what? Seems like it would be easier to just to change your feelings. Or would it?