Asya is an uncommonly occurring first name for women. Asya is also an uncommon last name for both adults and children. (2000 U.S. Census). Below is a graphed comparison of the popularity of the girl name Asya and corresponding names.opular alternative forms of Asya (not in Top 1000) listed in the Top 1000 are Aine, Aja, Ana (#222 last year) , Anika (#519) , Anissa, Anita, Ann (#945) , Anna (#34) , Anne (#553) , Anya (#472) , Asia (#806) , Hana (#841) , Nana, Nina (#295) , Nita and Nona. Variants like Ayn are seldom used.