Family name Бачкаі (Bocskay 
, Бачкаі 
) , in the world, is a rare last name. The cognomen Бачкаі is habitual in Hungary, where it is quite a rare surname, Romania, where it is a rare surname, and Austria. In absolute terms, this name is the most popular in Hungary, Romania, and the United States. Very seldom, Бачкаі is the forename as well as the last name.