Hamilton sits next to 4 phonetic neighbors — Harrison, Hammond, and Camden are the closest matches by sound. Most share Hamilton's Scottish cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"flat-topped hill settlement"
"visitor, pilgrim"
"lawman, legal authority"
"sky god, shining deity"
"fair, fair-haired, white"
"moon, moonlit"
"Dack's settlement"
"blond, white, bright one"
"son of Japheth, grandson of Noah"
"resolute protector"
"strong, hardy"
"huntsman, game warden"
"possibly fire-derived (East Asian linguistic inspiration)"
"goodness of God"
"rope maker"
"Yahweh is gracious"
"short form of Matthew"
"pine tree"
"little warrior"
"love, romantic feeling"
Similar sound: These names share phonetic patterns with Hamilton — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Old English/Scottish origins, giving them the same cultural heritage as Hamilton.
Rhythm: Hamilton is a 3-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.