Adding a calculated field on jpa + jackson - json

Question

How to add a calculated field to an entity?
DB table
table person {
id number,
first_name varchar,
last_name varchar,
...
}
Java entity
public class person {
BigDecimal id;
String firstName;
String lastName;
...//getters and setters
//what to add here???
public String getFullName() {
return firstName + " " + lastname;
}
}
I tried adding #Transient, but the field is ignored when converting to json.
I tried just leaving the method there, throws an exception that the setter is missing. adding the setter throws another exception that the field does not exist in the DB.
I tried adding #Transient and #JsonPropert, but the field is ignored when converting to json.
I tried adding #Formula, but hibernate (i think) says it is not implemented.
The idea is to have a simple calculated field that is ignored by jpa/hibernate but is used by jackson.
How can I accomplish this?
EDIT
Example full class
#Entity
#Table(name="FDF_PATIENT_COUNTIE")
#JsonIdentityInfo(generator = JSOGGenerator.class)
#JsonIgnoreProperties(ignoreUnknown = true)
#Audited
public class PatientCounty extends FgaBaseClass {
private static final long serialVersionUID = 1425318521043179798L;
private BigDecimal id;
private County FCounties;
private Patient patients;
public PatientCounty() {
}
public PatientCounty(County FCounties, Patient patients) {
this.FCounties = FCounties;
this.patients = patients;
}
#SequenceGenerator(name="generator", sequenceName="FDF_PATIENT_COUNTIE_SEQ")
#Id
#GeneratedValue(strategy=SEQUENCE, generator="generator")
#Column(name="ID", unique=true, nullable=false, precision=22, scale=0)
public BigDecimal getId() {
return this.id;
}
public void setId(BigDecimal id) {
this.id = id;
}
#ManyToOne(fetch=FetchType.LAZY)
#JoinColumn(name="ID_F_COUNTIE")
public County getFCounties() {
return this.FCounties;
}
public void setFCounties(County FCounties) {
this.FCounties = FCounties;
}
#ManyToOne(fetch=FetchType.LAZY)
#JoinColumn(name="ID_FDF_PATIENT")
public Patient getPatients() {
return this.patients;
}
public void setPatients(Patient patients) {
this.patients = patients;
}
}