Branson is a distinctive boys' name in United States, ranking #870 in 2008 with 244 recorded births. The name reached its all-time peak in 2014 with 377 births ranking #675. Since 1996, the popularity has increased by 95.2%. In 2008, approximately 1 in every 8,360 boys born was named Branson. FALLING Recent data shows the name is currently falling.