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"
"one who catches fish"
"ancestor descendant"
"from Laurentum; laurel-crowned"
"friend of Yahweh"
"vigilant in war"
"son of the sea (via Dylan influence)"
"high will, desiring much"
"little red-haired one"
"light"
"God has promised"
"village by the street"
"God is most high"
"from the brae (hillside) + lin (pool)"
"creative spelling of Rustin"
"from Brock's town, badger settlement"
"prophet, one who prophesies"
"phonetic blend (possibly new house, or river)"
"friend of the army, warrior's friend"
"raven, crow"
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.