Damary is a distinctive girls' name in United States, ranking #13411 in 2014 with 7 recorded births. The name reached its all-time peak in 2007 with 17 births ranking #7471. Since 1996, the popularity has increased by 40.0%. In 2014, approximately 1 in every 255,134 girls born was named Damary. FALLING Recent data shows the name is currently falling.