Yui sits next to 4 phonetic neighbors — Yuki, Yumi, and Rui are the closest matches by sound. Most share Yui's Japanese cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"to tie, to bind, connection"
"fictional warrior queen"
"twin"
"root child, sound child"
"zealous, zealot"
"king of the underworld (Japanese mythology)"
"self-arising"
"law, rule, model conduct"
"righteous talent"
"now go"
Similar sound: These names share phonetic patterns with Yui — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Japanese kanji 結 origins, giving them the same cultural heritage as Yui.
Rhythm: Yui is a 2-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.