Zoey is a variant, and is very much seen as "real". However, most people probably see
Zoe as the "correct" spelling. (I see it as a debate between
Catherine and
Katherine - both are seen as a proper spelling, but we all have opinions on which is "right")
I prefer
Zoe, mainly because I see the y as "wasting space", but I wouldn't say
Zoey isn't a name or incorrect spelling.