Monserrat is a distinctive girls' name in United States, ranking #703 in 2004 with 382 recorded births. The name reached its all-time peak in 2014 with 498 births ranking #592. Since 1996, the popularity has increased by 516.1%. In 2004, approximately 1 in every 4,807 girls born was named Monserrat. FALLING Recent data shows the name is currently falling.