Rima is a distinctive girls' name in England & Wales, ranking #4564 in 2009 with 4 recorded births. The name reached its all-time peak in 1996 with 24 births ranking #891. Since 1996, the popularity has decreased by 83.3%. In 2009, approximately 1 in every 78,344 girls born was named Rima. RISING Recent data shows the name is currently rising.