Branson is a distinctive boys' name in United States, ranking #1019 in 2002 with 151 recorded births. The name reached its all-time peak in 2014 with 377 births ranking #675. Since 1996, the popularity has increased by 20.8%. In 2002, approximately 1 in every 12,857 boys born was named Branson. FALLING Recent data shows the name is currently falling.