JPA many-to-one relationship CascadeType behavior

I have 2 tables: User and Loan. User have 3 fields: id (PK), first_name and last_name. Loan table have field user_id that is foreign key to User table:

The logic of my application: when I create new Loan object and set there a corresponding user it should create a new one for unique user or set a id of a user into user_id for existing user.

For that purpose my database have a unique index on first_name, last_name.

The Loan class uses User with @ManyToOne relationship:

public class Loan {
    @Id
    @GeneratedValue(strategy = GenerationType.IDENTITY)
    private Integer id;
    @ManyToOne(cascade = {CascadeType.PERSIST, CascadeType.MERGE})
    @JoinColumn(name = "user_id")
    private User user;
... methods ...

When I add new user, everything is fine, it persists to db with new PK. But when I try to add an existing one I got and exception:

javax.servlet.ServletException: org.springframework.transaction.TransactionSystemException: Could not commit JPA transaction; nested exception is javax.persistence.RollbackException: Exception [EclipseLink-4002] (Eclipse Persistence Services - 2.6.0.v20150309-bf26070): org.eclipse.persistence.exceptions.DatabaseException
Internal Exception: java.sql.SQLIntegrityConstraintViolationException: The statement was aborted because it would have caused a duplicate key value in a unique or primary key constraint or unique index identified by 'FIRST_LAST_NAME' defined on 'USER'.
Error Code: 20000

Again when I put @ManyToOne(cascade = CascadeType.MERGE) I'm able only to enter existing users, as only I pass a new one that is not persisted in DB I got an exception:

javax.servlet.ServletException: org.springframework.dao.InvalidDataAccessApiUsageException: During synchronization a new object was found through a relationship that was not marked cascade PERSIST: User{id=null, firstName='a', lastName='a'}.;

@ManyToOne(cascade = CascadeType.ALL) didn't work as well.

UPDATE

the code for insertion new Loan is:

user = userService.findByName(firstName, lastName);
        if (user == null) {
            user = new User(firstName, lastName);
        }
        loan.setUser(user);
        loanService.save(loan);

findByName() and save() methods are:

private EntityManager em;    
public User findByName(String firstName, String lastName) {
            TypedQuery<User> query = em.createQuery(
                    "SELECT u FROM User u WHERE u.firstName = :firstName " +
                            "AND u.lastName = :lastName", User.class)
                    .setParameter("firstName", firstName).setParameter("lastName", lastName);
            List<User> users = query.getResultList();
            if (!users.isEmpty()) {
                return users.iterator().next();
            } else {
                return null;
            }
        }

     public void save(User user) {
            if (user.getId() == null) {
                em.persist(user);
            } else {
                em.merge(user);
            }
        }