If you are entitled to court-appointed counsel, the court will give you Legal Aid, or if there is a conflict, an 18B attorney. You will not be permitted to choose the attorney if you are appointed counsel.
Please understand though that there are financial requirements before the court will appoint you an attorney. Discuss the matter with the judge and the Legal Aid screening office.
The above answer is intended for informational purposes and is not legal advice. It does not constitute the creation of an attorney-client relationship.
If you qualify for appointed counsel you get who the Judge assigns. If you hire a lawyer who can pick.
I am a former federal and State prosecutor and have been handling criminal defense and personal injury cases for over 17 years. The above answer, and any follow up comments or emails, is for informational purposes only and not meant as legal advice.