This lovely Hungarian girl name is a guilty pleasure of mine! In Hungarian it's pronounced ZHAW-nee-kaw (zh is the same sound as the French j, like in Jacques), but there I also love the pronunciation as ZHAH-ni-kah. Unfortunately, the Zs spelling renders it quite hard to use as an American name. I haven't been able to find the meaning. Perhaps it was created as a Hungarian variant on Anika?