I have no idea what you are using this for, but if you are making mythological references, always use Homeric Greek names. Your question isn't really about spelling, since you are never using "Greek spelling" in an English text, but rather nomenclature. The spelling is a set of conventions which poorly reflect the way those words were spoken.
Here's an example. Zeus/Jupiter. Looks like they have nothing in common, right? Until you remember that ptr is a very old morpheme signifying "father" (same word), which appeared in Latin as "pater".
Zeus in Greek would actually be pronounced DIOS
couple sounds got clipped along the way
So Jupiter=Io Pater
Zeus, father of Gods.
*this rough illustration is not scholarly and omits necessary caveats
So I don't know what you mean by it "sounds exotic." If you wish to use Greek names for non-Greek characters, the only other good reason is mythological allegory. I'm a big fan of that, personally.
Tossing it in randomly for no reason...well, that's about as good as it sounds.