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"
"sadness, melancholy"
"Dack's settlement"
"pure, innocent, clean"
"God has healed"
"rope maker"
"divine, godlike"
"royal dignity, greatness, grandeur"
"grandfather"
"American invented name with theophoric -jah suffix"
"homestead by the stream"
"peace"
"God prevails"
"he laughs, he will laugh"
"wheel maker, craftsman"
"knight, mounted warrior"
"enlightened, strong"
"God supports"
"lake of the sage Kashyapa (Sanskrit etymology)"
"island"
"hillside, river bank"
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.