Are you thinking of the netlist from "calibre -spice" during the LVS job?
The source names can't appear in that netlist, but I believe source names can eventually be shown in a new netlist created by using the Calibre CCI Querry Server. A related command used in that tool that may be helpful to you is LAYOUT NETLIST NAMES SOURCE. There are several other commands probably required to get what you want. I think you may find helpful information in the "Calibre Connectivity Interface" sections of the "Calibre Query Server Manual".
If you haven't already tried, your other option is to export a CDL netlist from Cadence (in the CIW, File -> Export -> CDL, I believe). CDL maintains the same net and instance names from your schematic and also maintains the hierarchy of the design. You can then use this netlist to run LVS against the corresponding layout.