Is it obligatory to fulfill a vow to name the newborn "Mahmoud" and to stop smoking cigarettes, given that the vow was made before separating from the first wife, and now the second wife is pregnant? And what is the ruling if the vow is not fulfilled and the newborn is given another name?

What we understand is that the questioner made a vow to name his son Mahmoud and to quit smoking if Allah blesses him with a boy. As for the vow to name him, it is not obligatory to fulfill it; rather, it is a permissible vow, and nothing is required for it according to the majority of scholars. As for quitting smoking, it is obligatory in all cases, as it is forbidden. If you violate the vow and smoke after being blessed with a boy, you must offer an expiation for breaking an oath, in addition to the sin of consuming tobacco. If your intention was to do so if you were blessed with a boy from a specific wife, and then you divorced her, then nothing is required of you from the perspective of the vow, and you must quit smoking in all cases.