Zasha is a distinctive girls' name in United States, ranking #13048 in 2014 with 8 recorded births. The name reached its all-time peak in 2009 with 16 births ranking #8052. Since 1996, the popularity has increased by 33.3%. In 2014, approximately 1 in every 223,242 girls born was named Zasha. FALLING Recent data shows the name is currently falling.