I found the Hungarian, female name "Zsanett" for you. It's close to your name, and appears to be a form of the name "Jeanette", as its meaning is "God has been gracious".
http://www.qj.com/babynames/Girl-z.html
I don't know if your name may have been the result of your godmother possibly mishearing the pronunciation of a similar-sounding name, or if your name comes from some African language with which your godmother may have been familiar. But if your godmother truly can't remember from whence she found that name, then who knows?
-- Nanaea