I don't know about Algerian law, but in the US, criminal cases usually have two phases. In the first phase, guilt or innocence is established. In the second phase, a penalty is set. The same judge usually presides. He/she hears arguments from both sides for leniency vs. stiffness. We call the second phase the penalty hearing. If the same applies in Algeria, then I would simply refer to the judge as "the judge at the penalty hearing" or the "penalty phase judge." It is not a formal title.

If a formal title is used in Algeria, I would use the expression "penal judge." I would not worry about تنفيذ. The judge does not implement the sentence, but merely defines it.

This judge has nothing to do with the judicial system and issuing sentences.

He represents the excutive authority, and has no right to protest or intervene.