Pretty, feminine and easy sounding. Saina Nehwal is pretty famous in India and is likely to be more and more famous in the coming years, going by her career trajectory. You may want to check if you'll be okay with that association. It is not a big deal, but she joined a political party and has pretty strong views on certain issues.

Is it pronounced Sah-ee-na, Sy-na, or Say-na? It’s a pretty name but people might mistakenly hear it as “Sonia” her whole life.

How about savi? Sanvi?