Rumi sits next to 3 phonetic neighbors — Remy, Lumi, and Rudi are the closest matches by sound. Most share Rumi's Japanese cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"lapis lazuli, beauty"
"eagle friend"
"spear servant"
"son of Ole (ancestor)"
"slender one"
"ripe, free"
"home ruler, lord of the estate"
"Ella's hill, Elli's hill"
"modern American invention combining Da- prefix with Marion"
"modern invented name with no fixed meaning"
"the foremost one"
"the immortal self"
"well-spoken, good word"
"curly-haired"
"son of Brice; son of Bryce"
"new house, bright (via Xavier heritage)"
"of the Chiel family"
"Yahweh has shown favor"
"the wild cat"
"to reap, harvest"
"broad, prosperous, grand"
Similar sound: These names share phonetic patterns with Rumi — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Japanese origins, giving them the same cultural heritage as Rumi.
Rhythm: Rumi is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.