Vasilios' root is Greek, and the name Vasilios means royal, kingly. Vasilios is a variant transcription of Basil (Greek): from the Greek name Basileios.Vasilas is a popular surname.asilios is an equally unique last name for all people. (2000 U.S. Census). Displayed below is a comparison of the popularity of the boy name Vasilios and related names.