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"
"glorious protector (as diminutive of Branislav)"
"second of twins"
"speckled, or from the bridge settlement"
"light, bringer of light"
"variant of Nile (great river)"
"in the beginning"
"pure, obedient"
"eternal, immortal"
"sun"
"new, fresh"
"from the sheep settlement, from Skipton"
"scholar, teacher (from Dutch Schuyler)"
"young warrior"
"God is gracious"
"coin, payment"
"island meadow, land near water"
"son of Thomas, son of the twin"
"wonder, sign"
"cloth merchant, fabric trader"
"Yahweh is merciful"
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.