There are instances of "reference fixing" where a proper name is attached to a description and so that the proper name is rigid. Consider "'Hesperas' shall be the name of the brightest non lunar object in the evening sky." Hesperas is a rigid designator.
There are also cases of the use of descriptions to fix non rigid references to proper names such as the example given here.
You find an old painting. After engaging in some convoluted discussion about legal ownership, you decide to clarify your terms: “Let the expression ‘Originalowner’ designate, for any possible world w, the original owner in w of that painting” (you point at the painting). You have causally grounded ‘Originalowner’ by means of a baptismal ceremony; but the referent varies from world to world, depending on who first owned the painting. The term is not rigid.
If 'God' is empty in this world, there is a possible world (it seems to me, the closest possible world to our's with only the relevant differences) where the description of him given in the Bible holds. The name will attach to that being through the description. It may be a weighted description of conjuncts. His leading of Moses and the Jews out of Egypt, being the Creator, being very powerful etc may all be taken into account as the description describing him in that world.
So if 'God' is an empty term, it will still refer to a non rigid possibilum in that ceteris paribus world. Talk of him will be like talk of Santa Claus, etc, meaningful in some sense but strictly speaking, empty. All subsequent talk causally related to the term and through intention ("Allah" e.g.) will designate such a possibilum. This is how we can talk about possibilia and make meaningful distinctions between fictional "truths" and "falsehoods" (Santa Claus has a beard and Santa Claus is a mouse, respectively, for example) and how we know we are "talking about the same thing" in conversations about possibilia. I will talk about the implications of this talk of possibilia as it relates to the (actual) status of our souls and to Pascal's wager in my next post.