Branson is a distinctive boys' name in United States, ranking #979 in 2000 with 152 recorded births. The name reached its all-time peak in 2014 with 377 births ranking #675. Since 1996, the popularity has increased by 21.6%. In 2000, approximately 1 in every 12,921 boys born was named Branson. FALLING Recent data shows the name is currently falling.