Kairi sits next to 3 phonetic neighbors — Kai, Cary, and Cairi are the closest matches by sound. Most share Kairi's Japanese cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"nautical mile, measure of sea distance"
"son of the twin"
"from the badger settlement"
"to hide"
"letter Z sound"
"thankful"
"young person, noble youth"
"dweller by the mills, mill worker"
"place of the Huxley family (surname origin)"
"handsome youth"
"swift, graceful"
"from Britain, a Briton"
"moon, of the moon"
"thunder, of Thor"
"from Dax, France"
"aromatic spice from nutmeg"
"farm on a hill, settlement by a mound"
"from Lucania, southern Italy"
"maker or seller of knives"
"possibly from Basque or Persian place names"
Similar sound: These names share phonetic patterns with Kairi — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Japanese origins, giving them the same cultural heritage as Kairi.
Rhythm: Kairi is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.