Hi ParaCAD,
There is a way to mirror a part then have it saved as a different name.
First you place the original part in an assembly (doesn't really matter where). Then you go "Insert", "Mirror Component". You will get a new properties window on the side. Select a mirror face (I usually select the plane inside the component), then the original component. Make sure the the check mark is checked in the "Components to mirror" box. Then hit the arrow (on the top). It will then prompt you for a file name and you can do that for the new part (and location too). Then click checkmark and you are done.
Keep in mind that your new mirrored part is linked to the original part. If you want to break the link, you can right mouse click on the mirrored component, then "List External References..." then "Break All". After you break the link, you will NOT be able to relink it.
Hopefully this is what you are looking for.
Allan Chun
SolidWorks 2005, CSWP