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The export creates a binary or JSON asset for each skeleton (having the export checkbox set) and the optional atlas and PNG files.
Binary and JSON assets are named using the skeleton name as indicated in the user guide.
The atlas and PNG files are instead named differently depending on the second drop down option. As per documentation:
Atlas per skeleton
An atlas is packed for each skeleton. Each atlas is named using the skeleton name, which matches the name of the corresponding skeleton data file.
Single atlas
The images for all the skeletons are packed into a single atlas. The atlas is named using the name of the project file without the file extension.
If you want to have your atlas text and PNG files named as the skeleton, you can select the Atlas per skeleton
option. Otherwise the project name will be used.