Java using filtering at different models before and after the projection

JPA Criteria API doesn't have such functionality. Also, it is not easy to read

JPA Criteria API

In the Criteria API you need to reuse the Expression.

The working code looks like this:

public List<PersonVO> findActivePersonByFullName(String fullName) {
  CriteriaBuilder cb = entityManager.getCriteriaBuilder();
  CriteriaQuery<PersonVO> cq = cb.createQuery(PersonVO.class);
  Root<Person> root = cq.from(Person.class);

  List<Predicate> predicates = new ArrayList<>();
  predicates.add(cb.equal(root.get("active"), true));

  Expression<String> fullNameExp = 
      cb.concat(cb.concat(root.get("firstName"), " "), root.get("lastName"));

  cq.select(cb.construct(
      PersonVO.class,
      root.get("id"),
      fullNameExp
  ));

  if (fullName != null) {
    predicates.add(cb.equal(fullNameExp, fullName));
  }

  cq.where(predicates.toArray(new Predicate[0]));

  return entityManager.createQuery(cq).getResultList();
}

The generated SQL code:

select
    person0_.id as col_0_0_,
    ((person0_.first_name||' ')||person0_.last_name) as col_1_0_ 
from
    person person0_ 
where
    person0_.active=? 
    and (
        (
            person0_.first_name||?
        )||person0_.last_name
    )=?

JPA Criteria API and @org.hibernate.annotations.Formula

Hibernate has an annotation org.hibernate.annotations.Formula that can simplify the code a little.

Add to the entity a computed field annotated with @Formula("first_name || ' ' || last_name"):

@Entity
public class Person {

  @Id
  @GeneratedValue(strategy = GenerationType.AUTO)
  public Long id;

  @Column
  public String firstName;

  @Column
  public String lastName;

  @Column
  public boolean active;

  @Formula("first_name || ' ' || last_name")
  private String fullName;

  //...getters and setters
}

And in the JPA Criteria API query reference the field fullName:

public List<PersonVO> findActivePersonByFullName(String fullName) {
  CriteriaBuilder cb = entityManager.getCriteriaBuilder();
  CriteriaQuery<PersonVO> cq = cb.createQuery(PersonVO.class);
  Root<Person> root = cq.from(Person.class);

  List<Predicate> predicates = new ArrayList<>();
  predicates.add(cb.equal(root.get("active"), true));

  cq.select(cb.construct(
      PersonVO.class,
      root.get("id"),
      root.get("fullName")
  ));

  if (fullName != null) {
    predicates.add(cb.equal(root.get("fullName"), fullName));
  }

  cq.where(predicates.toArray(new Predicate[0]));

  return entityManager.createQuery(cq).getResultList();
}

And the generated SQL:

select
    person0_.id as col_0_0_,
    person0_.first_name || ' ' || person0_.last_name as col_1_0_ 
from
    person person0_ 
where
    person0_.active=? 
    and person0_.first_name || ' ' || person0_.last_name=?

Hibernate Criteria API

Hibernate Criteria API (deprecated since Hibernate 5.2 in favour of JPA Criteria API) allows to use aliases. But not all databases allows to use aliases (e.g. (full_name || ' ' || last_name) as full_name) in a where clause.

According to the PostgreSQL docs:

An output column's name can be used to refer to the column's value in ORDER BY and GROUP BY clauses, but not in the WHERE or HAVING clauses; there you must write out the expression instead.

It means the SQL query

select p.id, 
      (p.first_name || ' ' || p.last_name) as full_name 
  from person p
 where p.active = true
   and full_name = 'John Doe'

doesn't work in PostgreSQL.

So, using an alias in a where clause is not an option.