Damary is a distinctive girls' name in United States, ranking #7471 in 2007 with 17 recorded births. The name reached its all-time peak in 2007 with 17 births ranking #7471. Since 1996, the popularity has increased by 240.0%. In 2007, approximately 1 in every 113,085 girls born was named Damary. FALLING Recent data shows the name is currently falling.