Hello,
The slot name is the name you specify after the [slot] tag and it won't take into account the folder path.
It should be noted that attachment name and slot name are two different things, and what you seem to be expecting is for attachment paths to be applied to slots.
Slot names don't usually have subfolder paths in them, if you look at the example projects that come with Spine, you'll notice no slot has a subfolder path. The image attachments inside them, however, do.
As slots exist to provide a flexible draw order in the draw order node, you'll end up seeing them listed there, therefore you likely may want to use unique names for the parts rather than numbers.
Here's links in case you'd like to know more:
Slots - Spine User Guide
Images - Spine User Guide
Attachments - Spine User Guide
Regions attachments - Spine User Guide