Hi Eric. Oh, sorry, I misunderstood you there.
You can have a look at the class AtlasAttachmentLoader which shows how to get rectangular uv coords from an Atlas based on a name string:
spine-runtimes/AtlasAttachmentLoader.cs at 3.7
So basically you will need a call like
AtlasRegion region = atlas.FindRegion(path); to query the region info of your sprite within the whole atlas image.
Then you can utilize Unity's means of copying texture regions to other textures, or map your own custom quad to this region by setting the region's uv coords, etc.
Please let me know if this is what you need!