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Here's names listed as used in Italian and Greek on BtN:
Anna
Clio
Irene
Maria
Marianna
Marina
Sara
Sofia / Sophia

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Also, here's a few names I found in my searching that are marked as used in Italian, but are the Italian form of a Greek name or form (there's probably more, I just scanned a few searches).
Dafne (Daphne)
Susanna
Angelica
Berenice
Catarina / Caterina
Daria
Elena
Teresa

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Otherwise one has Greek and the other Italian. Or a Greek first name and Italian middle name vice versa.
Anastasia and Bianca
Katerina and Emiliana
Helen and Teresa

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Anything there? Just keep searching till you find it.