Using `dom_id` means generating `new_document` as ID for new documents.
Since there might be more than one new document in the form, that means
duplicate IDs, which is invalid HTML.
Even though this issue doesn't affect image fields (because we don't
have many images on the same form), we're removing the ID there as well
for consistency.
We were using long, unique names because these methods used to be helper
methods. Helper methods should have unique names because otherwise one
method would overwrite the other.
Now that we're using components, we can omit the `image_` and
`document_` prefixes.
