Branson is a distinctive boys' name in United States, ranking #1017 in 2003 with 155 recorded births. The name reached its all-time peak in 2014 with 377 births ranking #675. Since 1996, the popularity has increased by 24.0%. In 2003, approximately 1 in every 12,744 boys born was named Branson. FALLING Recent data shows the name is currently falling.