Zasha is a distinctive girls' name in United States, ranking #8052 in 2009 with 16 recorded births. The name reached its all-time peak in 2009 with 16 births ranking #8052. Since 1996, the popularity has increased by 166.7%. In 2009, approximately 1 in every 114,804 girls born was named Zasha. FALLING Recent data shows the name is currently falling.