Rin sits next to 4 phonetic neighbors — Lynn, Lyn, and Wren are the closest matches by sound. Most share Rin's Japanese cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"companion, neighbor"
"dark, black"
"helper"
"dawn, aurora, morning light"
"from the hollow, hollow dweller"
"earth, land"
"God is my strength"
"sky, heaven"
"consecrated to God"
"courage, bravery (勇気)"
"praised, one who is praised"
"from Britain; British woman"
"maiden of strength"
"blue, indigo"
"modern invented name with Z-strength"
"lyric, of or relating to the lyre, suitable for singing"
"diminutive of Aodh (fire)"
"bearer of good news"
"eye, mirror"
"nobility, noble birth"
Similar sound: These names share phonetic patterns with Rin — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Japanese origins, giving them the same cultural heritage as Rin.
Rhythm: Rin is a 1-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.