I think you meant “not” sharing his name. Good. Don’t.
A court-assigned lawyer is a lawyer who had to pass the same Bar exam to be licensed to practice in the state as all other lawyers in the state did. The differences between a court-appointed attorney (aka public defender) and a private attorney can include trial experience (public defenders often have greater trial experience) and caseloads (public defenders often have several times the number of cases per year of a private attorney) and income (public defenders often make a fraction of what private attorneys make).
A private attorney often can devote more time to each individual case. This can be an advantage. However private attorneys can be costly. Public defenders are available to those who cannot afford the cost of a private attorney (e.g., are indigent).
You should trust that your friend will have good representation.