Cognomen Irai (Irai 
, Ирай 
, Iraí 
) , worldwide, is a rare last name. The cognomen Irai is habitual in Mexico, where it is a rare surname, Kyrgyzstan, and Norway, where it is a very rare surname. Not in comparison with a country's population, it is commonest in Mexico, India, and China. More prevalently, Irai is the forename as well as the last name.