* Ιωάννα (Ioanna): This is the most common and straightforward translation, derived from the Hebrew name "Yochanan" (John), of which Joan is a feminine variant. This is generally the best choice.
* Ιωάννη (Ioanni): This is a less common variant of the name, also derived from "Yochanan". It's used less frequently than Ioanna.
The choice between Ioanna and Ioanni is largely stylistic. Ioanna is the overwhelmingly preferred and more natural-sounding option in modern Greek.