Hamish sits next to 3 phonetic neighbors — James, Jamish, and Danish are the closest matches by sound. Most share Hamish's Scottish cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"supplanter"
"evergreen flowering shrub of the Mediterranean"
"sky father, king of the gods"
"son of Anne"
"dove"
"black-haired"
"bold warrior, warrior chief"
"grace, kindness"
"to travel leisurely"
"blessed, holy"
"treasurer, keeper of treasure"
"elf warrior (alternative etymology)"
"a rousing song of praise or national identity"
"thankful"
"little salmon, little goad"
"may He add"
"Athenian, of Attic culture"
"of high quality, excellent"
"long hill, ridge settlement"
"son of Andrew"
Similar sound: These names share phonetic patterns with Hamish — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Hebrew via Gaelic origins, giving them the same cultural heritage as Hamish.
Rhythm: Hamish is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.