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"
"the foremost one"
"slender, gentle, delicate"
"promised land, holy city"
"majestic, venerable"
"of the royal dynasty"
"lover of hounds"
"standalone phonetic name derived from letter sounds"
"Aromatic herb, salvia"
"immortal, deathless"
"muddy farm or settlement"
"gift of Yahweh"
"little dark one"
"the wild cat"
"buck's meadow, deer clearing"
"capable with a spear"
"modern invented name from Kyle + -er suffix"
"sky father, father of gods"
"white, fair-complexioned"
"servant of Marduk"
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.