Monserrat is a distinctive girls' name in United States, ranking #635 in 2005 with 441 recorded births. The name reached its all-time peak in 2014 with 498 births ranking #592. Since 1996, the popularity has increased by 611.3%. In 2005, approximately 1 in every 4,190 girls born was named Monserrat. FALLING Recent data shows the name is currently falling.