Meaning of Sioned. Welsh name. In Welsh, the name Sioned means-Welsh form of Jane: God is gracious. Gods gift.. Other origins for the name Sioned include-Welsh, Irish.The name Sioned is most often used as a girl name or female name.Welsh Name Meaning-Welsh form of Jane: God is gracious. Gods gift.ther origins for the name Sioned include-Welsh, Irish.The name Sioned is most often used as a girl name or female name. Welsh Name Meaning-Welsh form of Jane: God is gracious.