Branson sits next to 4 phonetic neighbors — Brandon, Bryson, and Grayson are the closest matches by sound. Most share Branson's English-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"son of Brand, son of the sword"
"bookbinder, scribe"
"God is gracious (via James/Jacob etymology)"
"God has been gracious"
"earnestness, sincerity"
"without wax, pure"
"in him there is strength"
"flame, fiery one"
"powerful counselor (via Ronald)"
"short form of Asher (happy, blessed)"
"bright"
"victory of the people"
"God is gracious"
"gentle, tamed"
"from the isle"
"noble lord"
"strong and courageous"
"god-helmet"
"inheritance, bequest"
"bold and modern (cultural meaning)"
"Yahweh saves"
Similar sound: These names share phonetic patterns with Branson — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Old English/Old Norse origins, giving them the same cultural heritage as Branson.
Rhythm: Branson is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.