Hi Will,
When you create a gallery you can specify the name. Also you can add meta information when you upload an image, like this

If you mean from the frontend, you can always specify captions for Aesop Images and Galleries. If you mean codewise, all Aesop components get auto-generated unique IDs when they are inserted into a post. You should be able to see them using an inspector on your browser. If didn’t understand your question fully, let me know.