Yes, such a change or "substitution of counsel" can be made. However while a defendant can request the substitution of a court appointed lawyer, the court does not have to allow it. There will need to be a hearing. That means that you can get a different attorney to represent you if you can convince the judge that it is necessary in order to adequately have your case presented. To seek a hearing for substitution of counsel, you will need to write a letter to the judge requesting a meeting (a copy should be sent to both the prosecutoer and the attorney that he you want removed).  Make sure the original/copies are sent certified mail, return receipt requested (you will also need to keep a copy for yourself). This letter should state that yoo want your current lawyer removed from you case and why. You need to list all problems that you have had with them. The letter should be kept short and to the point.  Be sure that it is truthful, you do not want to jeopardize your position before the judge by stretching the truth.