Hennessey is a distinctive girls' name in United States, ranking #7649 in 2005 with 15 recorded births. The name reached its all-time peak in 2015 with 27 births ranking #5037. Since 1996, the popularity has increased by 150.0%. In 2005, approximately 1 in every 123,180 girls born was named Hennessey. FALLING Recent data shows the name is currently falling.