It's a beautiful name, but I'm sure people would pronounce it wrong (it should be per-SEF-uh-nee, and I'd think that any educated person would pronounce it right, but I hear people say "Percy-phone" all the time) and she'd probably get Stephanie a lot. The meaning of this name is not certain. Most etymologists guess that it is related to the Greek words pertho ("to destroy") and phone ("murder"), but no one is entirely sure, so I wouldn't let the perceived meaning bother you much. I say go ahead and use it. It's a great name for a child born in the spring, because according to Greek mythology, seasons are controlled by Persephone's coming and going to and from the Underworld (where she lived with her husband, Hades), and spring would come whenever she returned.
Other names you might like:
Xanthe
Penelope
Ianthe
Danae
Eudora
Ione
Kalypso
Dione
Parthenope
Selene
Andromeda
Halcyone
Helene
Kalliope
Hope I helped!