THOMASSINA, THOMASSINE, and TAMZINE, are all feminine forms of Thomas:  the generally accepted meaning of this name is "a twin", and it is a traditional belief that the Apostle Thomas had a twin-sister called Lysia.
    On the other hand, some have derived the name from the Phoenician synonym of the sun-god—Thammuz—an idol which personified the sunshine, and was greatly beloved of Hebrew women, who worshipped him.  The prophet Ezekiel mourned over the idolatry of his countrywomen when he beheld them "weeping for Tammuz".  The festival held in honour of this deity took place some time in June, part of that month being named Tamus.  It is possible that in their veneration for the god, Hebrew women called their children after him; and that, later on in less idolatrous times, the name was handed down in families without any reference to or thought of its original significance. (Girls' Christian Names, Swan, 1905)