Damani is a distinctive girls' name in United States, ranking #4449 in 2003 with 29 recorded births. The name reached its all-time peak in 2012 with 40 births ranking #3865. Since 1996, the popularity has increased by 383.3%. In 2003, approximately 1 in every 63,002 girls born was named Damani. FALLING Recent data shows the name is currently falling.