Rima is a distinctive girls' name in England & Wales, ranking #2547 in 2016 with 10 recorded births. The name reached its all-time peak in 1996 with 24 births ranking #891. Since 1996, the popularity has decreased by 58.3%. In 2016, approximately 1 in every 30,714 girls born was named Rima. RISING Recent data shows the name is currently rising.