You can set a name for the atlas, so then you'd only need to rename the data file:
Spine -i <path> [-j <path>]... -o <path> [-n <name>] -p <path>
If you are packing as part of data export, you can easily pack separately. Hmm, unless you are using the option to pack only the attachment images that are in use, that is only available as part of data export.
Options in the export setting JSON are a possibility, but relying on the position isn't great. Might be better to allow a single name in the JSON, and error if there is more than one skeleton.
Really the best solution is to have your animators name their skeletons appropriately. 🙂