Zooey looks like it rhymes with gooey... cute to have a slightly childish name if you make a career off being cute, like Deschanel, or if you're a character in a story about thinking - maybe not so cute if you're just a regular person. YMMV but I'd leave the particular kind of flakiness of "Zooey" to the flakes.
Zoey is not so bad since it seems like it's meant to head off people who'd pronounce
Zoe as "Zo" but I think it also looks sort of childish.
Zoe is the only spelling I'd use (or wish to bear).