Gracious
Jaynee is a modern phonetic variant of Janie, which is a diminutive of Jane. It ultimately derives from the Hebrew name Yochanan, meaning 'God is gracious,' and has evolved through various European languages before becoming a staple in English-speaking countries.
Less common today
Jaynee isn't in the latest US Top 1000. It last peaked at #5,451 in 1991.
US births per 5-year period, 1990βpresent (SSA data).