I think a macro is the way to go.
I'd go ahead and have the data card create a unique number for each configuration, link that number to a configuration specific file property, then use the configuration object.name API property to rename the configuration to the configuration specific file property.
Here is an example of working with the configuration object that will get you most of the way there: http://help.solidworks.com/2015/english/api/sldworksapi/Change_Configuration_Properties_Example_VB.htm
I have my configuration's number generated by EPDM data card stored in the custom property "Drawingnumber"
I don't know VBA, it's hard to find how to build a macro that will get the value renaming the configuration associated.
The best result will work automatically when creating the part or assembly or when adding a configuration.
Like do teamcenter integration (swim).