Surname Irii (Ирий 
, Irii 
, Ирии ) , around the globe, is a very rare cognomen. The cognomen Irii is habitual in Kazakhstan, where it is a very rare surname, New Zealand, and Russia, where it is an extremely rare surname. In absolute terms, it is the most numerous in Russia, Kazakhstan, and India. More frequently, Irii is the forename as well as the last name.