The name IS Hungarian and many girls/women bear that name in Hungary and in regions neighbouring that country. It is said that it's the result of the "Hungarization" of the Latin/Italian name Felicita(s) (English >Felicity) which means happiness and luck. The Latin appearance of the name Felicita must be at least 2000 years ago. The Hungarian form Zita might be from somewhere around 5th-8th centuries when the Magyars (now called Hungarians) began to travel closer to "Europe", or 8th-10th century when those Magyars settled down in the ex-roman province Pannonia, later to become Hungary. Because all over those periods they of course had many contacts to their immediate neighbours, the Italians/Latins/Romans.