No. Ancient Greek deities have historical/iconographic symbols (e.g., Zeus: thunderbolt, eagle; Athena: owl, aegis; Poseidon: trident), but there are no "modern" symbols created or recognized in contemporary religious practice.
Hellenic polytheism today (Hellenismos) uses reconstructed ancient symbols, not new ones. Neopagan or pop-culture inventions (e.g., Percy Jackson logos, graphic designs) are not canonical.
Greek mythology is studied academically, culturally, and artistically—not as a living state religion with evolving iconography.