Cognomen Šukaj (Шукай 
, Šukaj 
) , throughout the world, is a very rare last name. The family name Šukaj is habitual in Kazakhstan, where it is a rare surname, Croatia, where it is a very rare surname, and Russia. In absolute terms, this name is the most popular in Russia, Kazakhstan, and Ukraine. Very seldom, Šukaj is the forename as well as the last name.