Can psychodynamic psychotherapy and psychoanalytical psychotherapy permanently change the personality of a person?

Yes, hard to prove: It is certainly the aim of these psychotherapies to change fundamental personality traits (for the better of course). Countless case reports attest to success in doing so. But strong scientific proof would require careful, repeated personality assessment for large numbers of patients over many years — "permanently" is a long time — something that is very hard and expensive to study.

Yes: Undesirable or problematic aspects of one's personality can be changed with many types of therapy, including psychodynamic, where--as intrapsychic conflicts and resulting defense mechanisms are uncovered--increased self awareness can improve relations with self (ie self esteem) and others.

No, but...: Psychoanalysis and psychodynamic therapies understand the basic structure of the personality to be based on inherited factors and then shaped in childhood. However, there are more or less adaptive and satisfying ways that personality can be expressed. These therapies aim at maximizing this kind of adaptation.

Some research: On this question of the effect of psychotherapy: http://ajp.Psychiatryonline.Org/article.Aspx?Articleid=1688271 both cbt and psychodynamic therapy (and psychoanalysis) can help patients depending on the goals of the patient.

Impact: I am a psychoanalyst, and I believe psychoanalysis can have a major impact on a patient's personality and change it to a certain extent, but not to the point of totally transmogrifying them into someone unrecognizable by those near and dear to them. Effects of psychoanalysis are typically very long lasting and positive.

Analytic therapy: Analytic dynamic therapy is directed to the resolution of inter psychic and intrapsychic conflict, such as between desires or wishes and fear. Personality is much broader and involving non conflictual elements.