Last name Туи (Tui 
, Tooey 
, Туи 
) , in the entire world, is quite a common surname. The family name Туи is characteristic of Fiji, where it is quite a common surname, Malaysia, where it is quite a rare surname, and Estonia. In absolute terms, the name is most common in India, Malaysia, and Bangladesh. Likewise, Туи is the forename as well as the last name.