Branson is a distinctive boys' name in United States, ranking #949 in 2004 with 177 recorded births. The name reached its all-time peak in 2014 with 377 births ranking #675. Since 1996, the popularity has increased by 41.6%. In 2004, approximately 1 in every 11,214 boys born was named Branson. FALLING Recent data shows the name is currently falling.