A lot depends on the particular charges the defendant faces, exactly what is said, and the laws of the state in which the prosecution is taking place, and you did not mention a state. In general all telling a jury that the defendant’s lawyer is a public defender does is tell the jury that the defendant has insufficient means to pay for a lawyer himself/herself. Unless that fact is somehow relevant to the crime that the defendant is accused of committing I don't see any harm to the defendant in having the jury know his/her lawyer is a public defender. What kind of prejudice are you thinking occurs here?

