I was trying to do that, but with the code I was using it would not allow it, kept erroring out. I could give you more details once I am back at work in a few days, but from what I can remember the part that was erroring out was during the actual rename...
(keep in mind I am trying to do this from memory so might not be entirely accrate on the command)
fso.namefile "pathtofilelocationIwanttocopy\from.pdf", "pathtofilelocationIwanttoputthenewfileinto\" & Format(Date()-1, "mm/dd/yyyy") & "Contractor Packet.pdf"
Anyway in a few days I can give better information if this is not enough to get us moving in the solution direction again.