Hennessey is a distinctive girls' name in United States, ranking #6324 in 2004 with 19 recorded births. The name reached its all-time peak in 2015 with 27 births ranking #5037. Since 1996, the popularity has increased by 216.7%. In 2004, approximately 1 in every 96,638 girls born was named Hennessey. FALLING Recent data shows the name is currently falling.