Hennessey is a distinctive girls' name in United States, ranking #5966 in 2009 with 23 recorded births. The name reached its all-time peak in 2015 with 27 births ranking #5037. Since 1996, the popularity has increased by 283.3%. In 2009, approximately 1 in every 79,864 girls born was named Hennessey. FALLING Recent data shows the name is currently falling.