What does Shai mean?
From Hebrew shai 'gift'. The 'gift' meaning is widely cited, though the origin is disputed: some sources derive the name instead as a diminutive of Yeshayahu (Isaiah), 'God is salvation'.
What does Zion mean?
From Hebrew 'Tziyyon', the name of a hill in Jerusalem that came to stand for the city, the Promised Land and a place of peace. A long-standing biblical/geographic name now popular as a given name.