Branson is a distinctive boys' name in United States, ranking #932 in 1999 with 157 recorded births. The name reached its all-time peak in 2014 with 377 births ranking #675. Since 1996, the popularity has increased by 25.6%. In 1999, approximately 1 in every 12,230 boys born was named Branson. FALLING Recent data shows the name is currently falling.