The depositor value for an EPrints uses the EPrints Users values. I don't think it is a good idea to expose this part of the REST API. On the other hand users are not frequently added or remove and EPrints provides an easy way to dump a user list which we can leverage when resolving the EPrint XML with who created the item.
Authenticate into your EPrints repository as a repository
administrator. Click on the "Admin" link, Click on the "Search Users"
button, Check all the User Type check boxes and press the search button.
This will give you a results list. For the export option from the
results pick JSON (or the whatever format you like working with).
The resulting page can be saved and is available to integrate
into your application when decoding the EPrint XML values
for userid.