How can I get the session object if I have the entity-manager?

See the section "5.1. Accessing Hibernate APIs from JPA" in the Hibernate ORM User Guide:

Session session = entityManager.unwrap(Session.class);

'entityManager.unwrap(Session.class)' is used to get session from EntityManager.

@Repository
@Transactional
public class EmployeeRepository {

  @PersistenceContext
  private EntityManager entityManager;

  public Session getSession() {
    Session session = entityManager.unwrap(Session.class);
    return session;
  }

  ......
  ......

}

Demo Application link.

To be totally exhaustive, things are different if you're using a JPA 1.0 or a JPA 2.0 implementation.

JPA 1.0

With JPA 1.0, you'd have to use EntityManager#getDelegate(). But keep in mind that the result of this method is implementation specific i.e. non portable from application server using Hibernate to the other. For example with JBoss you would do:

org.hibernate.Session session = (Session) manager.getDelegate();

But with GlassFish, you'd have to do:

org.hibernate.Session session = ((org.hibernate.ejb.EntityManagerImpl) em.getDelegate()).getSession(); 

I agree, that's horrible, and the spec is to blame here (not clear enough).

JPA 2.0

With JPA 2.0, there is a new (and much better) EntityManager#unwrap(Class<T>) method that is to be preferred over EntityManager#getDelegate() for new applications.

So with Hibernate as JPA 2.0 implementation (see 3.15. Native Hibernate API), you would do:

Session session = entityManager.unwrap(Session.class);

This will explain better.

EntityManager em = new JPAUtil().getEntityManager();
Session session = em.unwrap(Session.class);
Criteria c = session.createCriteria(Name.class);