Branson is a distinctive boys' name in United States, ranking #675 in 2014 with 377 recorded births. The name reached its all-time peak in 2014 with 377 births ranking #675. Since 1996, the popularity has increased by 201.6%. In 2014, approximately 1 in every 5,094 boys born was named Branson. FALLING Recent data shows the name is currently falling.