Possible Greek-sounding alternatives that capture the essence of "pure" or "clean" include:
* Καλλιστώ (Kallistō): This means "most beautiful," which can be associated with purity.
* Αγνή (Agnē): This means "pure" or "holy."
* Καθαρά (Kathará): This means "pure" or "clean."
You wouldn't transliterate "Caitlyn" phonetically, as that would result in something sounding quite foreign in Greek. Instead, you would choose a name with a similar meaning or sound that fits within the Greek naming conventions.