米 (mǐ, "rice") is a stock transliteration character for foreign "Mi-" sounds — see
米兰 Milan,
米歇尔 Michelle,
米老鼠 Mickey Mouse.
姬 (jī) means "concubine / beauty" classically and is used as a female-name suffix in Japanese-derived transliterations (e.g.
由纪 →
由姬).
米姬 most often renders Japanese みき (Miki) or English Mickie/Mikki.