When a court appoints an appellate attorney, that appointment comes through the Public Defender's office. The inmate does not get to choose who is assigned, the court makes that determination and the Public Defender's office handles the assignment from there.
Finding out who was appointed is usually straightforward. The inmate can ask their case manager or counselor at the facility, who can help them contact the court clerk's office for the jurisdiction where the appeal is being filed. The clerk's office will have the attorney of record on file once the appointment has been made. The inmate can also write directly to the court asking for that information.
On the question of speaking with the attorney before anything is filed, yes, that opportunity exists and the inmate should absolutely use it. Appellate attorneys are required to communicate with their clients before filing, and the inmate has both the right and the practical need to be involved in building the appellate argument. They know the details of their case better than anyone, and a good appellate attorney will want to hear their account of what happened at trial, what they believe went wrong, and what issues they think are worth raising on appeal.
The inmate should be proactive about making contact once they know who has been assigned. Write a letter to the attorney introducing yourself, outlining the key issues as you see them, and requesting a meeting or a call. Public defenders carry heavy caseloads, and the clients who engage early and clearly tend to get more attention than those who wait passively for something to happen.