Rui sits next to 3 phonetic neighbors — Ruy, Louie, and Dewey are the closest matches by sound. Most share Rui's Portuguese-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"glorious ruler"
"love of God, God's beloved"
"of noble birth"
"generous, tolerant"
"given by Yahweh"
"gift of God"
"flax, linen plant"
"lapis lazuli, beauty"
"bean grower, of the bean family"
"defender of men"
"wise protector"
"bright color, vitality"
"one who has renewed life"
"talented, gifted"
"supplanter (via Jacob/James)"
"star"
"sky"
"great adviser"
"boundary, border"
"who is like God (form of Michael)"
Similar sound: These names share phonetic patterns with Rui — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Germanic via Portuguese origins, giving them the same cultural heritage as Rui.
Rhythm: Rui is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.