Damani is a distinctive girls' name in United States, ranking #4297 in 2009 with 35 recorded births. The name reached its all-time peak in 2012 with 40 births ranking #3865. Since 1996, the popularity has increased by 483.3%. In 2009, approximately 1 in every 52,482 girls born was named Damani. FALLING Recent data shows the name is currently falling.