Allvar \a-ll-var\ as a boy's name is a variant of Alvar (Old English), and the meaning of Allvar is "elf or magical army, warrior". The baby name Allvar sounds like Alvaro and Alavaro. Other similar baby names are Allgar, Alamar, Alomar, Alvan, Allger, Algar, Alltair, Alva, Alvah, Allmer, Aylmar and Halvar.