Gracious
Shenee is most commonly understood as a phonetic variation of Sinead, the Irish form of Janet or Jane. It ultimately derives from the Hebrew name Yochanan, meaning 'God is gracious'. While rare in this specific spelling, it shares its etymological roots with many classic Western names.
Less common today
Shenee isn't in the latest US Top 1000. It last peaked at #4,586 in 1991.
US births per 5-year period, 1990βpresent (SSA data).