Yui (結 or 唯) is a Japanese name with multiple kanji possibilities. The character 結 means "to bind" or "to tie" — implying connection and unity. The character 唯 means "only" or "unique." Families choose the kanji that fits the meaning they want.
Yui has been one of the most popular girl names in Japan for the past two decades. Two syllables, soft consonants, and a meaning that emphasises either connection or uniqueness, depending on the kanji.
Yui reduces to one — the number of unique presence.