Can a defendant switch to a different public defender?

Yes, such a "switch" can be made. It is called "substitution of counsel". However while a defendant can request the substitution of a PD a court does not have to allow it. There will need to be a hearing on this matter.  That means that he can get a different lawyer to represent him if he can convince the judge that it is necessary in order to adequately have his case presented. 

To seek a hearing for substitution of counsel, he will need to write a letter to the judge, requesting a meeting with them.  A copy should be sent to both the attorney that he wants removed. In addition the prosecutor.  Make sure both copies and the original (which goes to the judge) are sent certified mail, return receipt requested (RRR). He will also need to keep a copy for himself. This letter should state that he wants his current PD removed from his case and why.  He needs to list all problems that he had/is having with his lawyer. The letter should be kept short and to the point.  Be sure that it is truthful, he does not want to jeopardize his position before the judge by stretching the truth.