Here are a few modern Tamil girl baby names:

 Aadhya - First power, beginning

Aanya - Graceful

Aditi - Boundless, free, the earth

Aishwarya - Wealth, Prosperity

Akshara - Letter, symbol

Diya - Bright, shining light

Kavya - Poetry, literature

Nitya - Eternal, forever

Rhea - Flow, ease

Sia - God's gift, Grace of God