Hi,

Unfortunately, it is not possible to decide the naming of the atlas pages as you like or based on the folder name on the Spine editor. We have discussed several solutions to this in past posts, which we hope you will find helpful:
Deterministic (or editable) names for exported texture files
Mix and match outfits + Addressables loading issue

Hello! May I however suggest an alternative workflow:
You can pack your images into separate atlases by organizing them in the folders so that one folder corresponds to an atlas page you'd like to get. You can then use texture packer to pack the images folder respecting the folder structure if you place a pack.json file in each folder (which also has the big advantage of allowing you to even have different packing settings for each generated atlas page!)

Below are the relevant user guide entries for your case:

Texture packing - Spine User Guide: Folder structure
Texture packing - Spine User Guide: JSON Configuration

Thank you for sending your project, I found some causes that importing exported files to Unity will fail. I recommend that you read the user guide again, as you probably do not understand many of the settings correctly.

To solve the error, please do the following:

• Uncheck Combine subdirectories in texture packer settings window.
  This setting is used when you want to combine all subdirectories into a single page, but in your case, you should uncheck this since the pack.json files define the pages.

• Delete empty "pack.json" files in the "character_assets" folder.
  To begin with, you have set the pack setting to Image folder in your JSON export settings, so the texture pages will be created for each folder without pack.json. The complication was because you checked Combine subdirectories in your texture packer settings. This is a conflicting setting, so let's clear that up once. I confirmed the empty pack.json files in the "character_assets" folder are unnecessary except for the following two:
  ・The pack.json in the "armors > 01_cloth_male" folder
  ・The pack.json in the "male" folder
  In these two pack.json, write the following JSON:

  {
      combineSubdirectories: true
  }

  The JSON above allows images from a particular subdirectories to be combined into a single page.

• Uncheck Flatten paths in texture packer settings window.
  When Flatten paths is checked, subfolders are stripped from region file names in the .atlas.txt file.
  
  This option is used for a case when you want to set up skins by code in Unity. In your case, there is no need to check this option since you have set up skins on the Spine editor and want to use them as are.

• Uncheck Export for each "ref" attachments in the Tree view.
  Uncheck the Export checkbox in all skins. These images will be ignored during export by pack.json, but the settings in the editor make them eligible for export, resulting in an error as "missing regions".
  

When you have done the above, you should be able to import correctly. If something is going wrong, please let us know!

I'm glad to hear that it worked well
If there is something unclear in the user guide, please feel free to post them in this forum!

We don't normally dive into user projects if it can be avoided. It sounds like you just need to use Skeleton setAttachment. See that link for the API reference. See here for runtime docs:
Runtime Skeletons - Spine Runtimes Guide: Changing attachments
And here for spine-unity docs:
spine-unity Runtime Documentation: Setting Attachments