Damary is a distinctive girls' name in United States, ranking #7142 in 2002 with 15 recorded births. The name reached its all-time peak in 2007 with 17 births ranking #7471. Since 1996, the popularity has increased by 200.0%. In 2002, approximately 1 in every 119,788 girls born was named Damary. FALLING Recent data shows the name is currently falling.