Family name Bodai (Bodai , Бодай , بوداي ) , around the globe, is quite a rare surname. The surname Bodai is habitual in Hungary, where it is quite a rare surname, Bahrain, and Ghana, where it is a rare surname. Measured by absolute frequency, the name is most common in Hungary, India, and Japan. Likewise, Bodai is the forename as well as the last name.