Actually, you shouldn't get documentManager inside a document. Always get DM via ServiceLocator and use it in your Services/Models/Controllers. Persisting documents via DM on controller level is not a good practice. Controllers should consume related service/model interfaces to do that.
For your question, models and/or services should implement ServiceLocatorAwareInterface and properly configured to use SM.
If you need DM in every service/model instance, simply write a factory or initializer for that. Form the documentation:
Initializers : You may want certain injection points to be always
called. As an example, any object you load via the service manager
that implements Zend\EventManager\EventManagerAwareInterface should
likely receive an EventManager instance. Initializers are PHP
callbacks or classes implementing
Zend\ServiceManager\InitializerInterface. They receive the new
instance, and can then manipulate it.
Also this SO answer explain details how to do that (getting EM in services) with EntityManager but logic would be same for DocumentManager.