Generally speaking, you are not entitled to a specific public defender. The public defender's office that handles your case will assign an attorney to represent you. It may not be the attorney you'd like.
It never hurts to ask, however. If you have a good reason to want a specific public defender, the court may indulge your request, particularly if you have been represented by that lawyer before, as that lawyer will be in the best position to understand your case and advise you.
You can always ask, but generally your desires in this regard will not be followed. Colorado has a state public defender system with a good reputation. The office will be appointed and decide which attorney to assign your case to. It is a function of the number of cases the office has, the number of cases the individual public defender's have, the severity level of your charge, and other factor which impact the work load of the public defenders in the office.
Most public defender's offices will not accommodate requests for a particular public defender because of the difficulties it causes resource management within the office.
This answer is intended to provide general information about the justice system. It does not provide legal advice or create an attorney-client relationship. It does not provide the basis for making decisions about a course of action. Legal advice requires much more communication and information than is possible in this format. Many important considerations and factors need to be investigated and discussed before an attorney could give legal advice about this issue. Before making any decisions about a course of conduct readers are strongly encouraged to contact a lawyer and secure an attorney-client relationship.