Are there computer searches for new theoretical minerals in a similar vein to Folding@Home or SETI@Home?
By Ross Snider's request, I have moved my comment into an answer - whilst it does not address computational searches for minerals, it touches on the complexities of actually getting a mineral officially named:

The International Mineralogical Association Commission on New Minerals, Nomenclature and Classification seems to require a physical specimen for consideration for official naming of a new mineral. Under current rules, anthropogenic minerals are also excluded, so if you came up with a hypothetical mineral it seems you would have to also find a naturally occurring specimen to get it named.

To add to this, I am not aware of any software for systematically searching for plausible minerals, however computational packages for the simulation of crystalline structures certainly exist. Determining the electronic structure of a crystal - which is what is really required to make conclusions about geometry, stability and so on - generally involves the use of plane wave QM codes such as VASP, CASTEP or ABINIT, the latter of which is free. The feasibility of mineralogical calculations using these methods is strongly dependent on how crystalline the mineral is and how ideal it is (from a perspective of not being heavily defected or substituted) as they work within the constraints of a periodic unit cell or supercell.