Hello Tiago,
Please forgive the lag in my response. Your initial post coincided with my departure from California for Connecticut and New York City, a two week vacation with my wife and godson, which kept me away from the forums.
An argument could be made for each of the three terms you propose. I’m a little reticent about Symbolic Mythology, which may be overly broad: symbolism is embedded in every myth, so might not do enough to distinguish Campbell’s approach in a reader’s mind.
Personally, I like Perennial Mythology, but can see how that might require a detailed Perennial Philosophy 101 tutorial, as understood by Alduous Huxley and Ananda Coomaraswamy, or Marsilio and the neo-Platonists, among others.
Depth Mythology is apt, but could be just as difficult to explain (despite the resonance with depth psychology, most people, even those who have heard of Freud or Jung or Adler or Hillman and others, do not necessarily know what depth psychology is).
One possibility I could see is calling Campbell’s approach Archetypal Mythology – particularly given Campbell’s emphasis on recurring mythological motifs in myths across cultures. Many people who have never heard of the Perennial Philosophy or Depth Psychology have at least a vague notion of the term “archetype,” which is central to Campbell’s understanding, and relatively easy to explain (everyone understands the idea of “patterns” – I think of Ruth Benedict’s epic Patterns of Culture.)
But the term I’ve personally used most frequently the past couple decades to describe Campbell’s approach is Experiential Mythology. A living myth is not just an abstract tale, but the warp and woof of a culture – the fabric of life, as experienced by members of that culture. Similarly, Campbell’s emphasis on the Hero’s Journey and discovering one’s personal mythology is focused on the actual experience of the mythological dynamics of one’s life.
Obviously, “experiential mythology” has not caught on. I expect a generally accepted term will emerge over time, but imagine it will more likely be something Campbell-centric (in the way people refer to Jungian psychology, even though that’s a subset of depth psychology): maybe the Campbellian school of myth . .