Thea actually means "Goddess". Each goddess would have her own name, but they were all goddesses if you see what I mean. It isn't the special name of just one of them - that would be like naming your daughter Daughter or your dog Dog. Not helpful for telling 'em apart from the others ...
Dorothea means Gift of God, and
Thea is the short form. However, if you wanted to use a name meaning Gift of God for a boy, you'd end up wtih Dorotheus to make it a male name (like
Julius for a boy,
Julia for a girl). The -us ending doesn't refer to the god here, but to the boy whose name it is; similarly
Dorothea for a girl doesn't necessarily mean Gift of the Goddess; it's got a feminine ending to refer to the girl it belongs to.
Hope that helps!