Gemara

52a (Beraisa - R. Meir): "Es Aviha Hi Mechaleles" teaches that we no longer treat her father honorably (like other Kohanim). We say 'cursed is the one who fathered such a girl, who raised such a girl.

(Rav Ashi): Even if a Rasha's father is a Tzadik, we call him a Rasha ben Rasha. This is like R. Meir.

104a: "V'Ein mi'Yadi Matzil" - Avraham does not save Yishmael (from punishment), and Yitzchak does not save Esav.

Yoma 38b: Regarding Ben Kamtzar and his colleagues it says "v'Shem Resha'im Yirkav".

(R. Elazar): This teaches that we do not name people after them.

Rishonim

Question: According to the opinion that Avraham does not save Yishmael, why were righteous Kohanim Gedolim and Tana'im given this name?

Answer (Ritva Yoma 38b DH d'Lo and Tosfos Yeshanim DH Ma'ase): Since Hash-m said that this name should be given to Yishmael we are not concerned. Alternatively, R. Elazar holds like the opinion that Yishmael did Teshuvah (Bava Basra 16b).

Teshuvas ha'Rosh (17:12): Shimon, Yosef's father, became a Mumar to Islam. Yosef started calling himself Yosef ben Shmuel. He wrote this name in a Get. Rabanan were Machshir it. I do not understand why. One may change his own name; this can be Mevatel a decree (Rosh Hashanah 16b). However, one cannot change his father's name! People who see the Get will say that she is not divorced, for her husband's father is Shimon, and not Shmuel.

Terumas ha'Deshen (2:184): The Rosh disqualified due to errors (lest people think that she is not divorced). This is unlike changing the place of birth, which the Ri is Machshir. There no error will occur, for there was no need to write it. Also, perhaps the Rosh discusses one who did not intend to change his name. He called himself by his grandfather'sname, for grandchildren are like children. Even so, it is Pasul due to errors.

Yam Shel Shlomo (Gitin 4:21): Mahari of Ribork said that we call a Mumar's son to the Torah by his grandfather, like 'bar bar Chanah.' However, in a Get one should write the Yehudi name and every other name he is called. B'Di'eved, if they wrote the grandfather's name, she is divorced; we can learn from Rabah bar bar Chana. Presumably, the Rosh discusses when the grandfather was Shmuel. If not, why did Yosef pick that name?! There are other names closer to Shimon, e.g. Shemayah (the first three letters are the same)! The Rosh did not explicitly argue with those who were Machshir. He just expressed surprise. Therefore, the primary opinion is Machshir. (Note: perhaps the Rosh was surprised why they were Machshir without concern for how she will prove that she is divorced.) He did not change his name, he just calls himself by his grandfather's name. It is proper to be called to the Torah this way. A Get should be clarified better, but b'Di'eved it is Kosher. In a Teshuvah of Rashi, Yosef ben Yakov called himself Yosef ben Shmuel, for his father became a Mumar. Rashi was Machshir, for he had become established by this name. It was enacted (Gitin 34b) to write in Gitin 'Ploni ben Almoni and every name that I and my fathers have.' Chachamim did not require witnesses to establish his name and his father's. He may establish them himself. Rashi was Machshir because she already remarried. If not, he would have required another Get. If he was established to be called to the Torah by his grandfather's name, I would be Machshir b'Di'eved (to use the Get) even before the Get was given, if there is concern for Igun (inability to remarry).

Sefer Chasidim (791): If Ploni's father is a Mumar, we do not call him to the Torah in the name of his father, for it says "Es Aviha Hi Mechaleles" (and all the more so if the father himself sinned). If Ploni is a Chasan, who is called to the Torah, or if he must sign a document, he is called by his grandfather's name. If also his grandfather is a Mumar, he is called by his great grandfather.

Poskim

Rema (OC 139:3): If one's father is a Mumar, we call him to the Torah using his grandfather's name in place of his father's name. We do not call him only by his name, lest this shame him in public.

Terumas ha'Deshen (21): We call a Rasha's son to the Torah in the name of his grandfather, like Korach's son is called "Avi'asaf ben Yitzhar." One Rav said that we call him by his name alone. I disagree. This is shameful that he is called differently than others. We also find that it says "Lavan ben Nachor" and "Mefivoshes ben Sha'ul."

Rema (ibid): If he was used to being called by his father's name and his father became a Mumar, we continue to call him this way, lest we shame him in public.

Maharam Padova (87): The Terumas ha'Deshen would agree to this law. It is better to be burned than to publicly shame someone! Kavod ha'Briyos overrides a Lav of the Torah. All the more so it overrides v'Shem Resha'im Yirkav, which has no source in the Torah or Nevi'im. The verse teaches not to call a son by a Rasha's name, and to curse a Rasha when mentioning him, but one may call his son 'Ploni ben Almoni.' This is whether the son is a Rasha, like the sons of Yarav'am and Achav, or a Tzadik, like Chizkiyah ben Achaz. Since a Rasha's father is also called a Rasha, why does Terumas ha'Deshen permit calling in the name of the grandfather? We should call the son only by his own name! We do not, lest this embarrass him. The Rosh says that we call a Mumar's son to the Torah in the name of his father! This must be when he was used to being called this way, and the Terumas ha'Deshen discusses when he was not, e.g. the father became a Mumar before the son matured. We can also permit due to Darchei Shalom. Our custom is that the Shali'ach Tzibur holds the Sefer Torah and blesses the king. Shimon ha'Tzadik told Alexander Mukdan 'we pray for you in this house (the Beis ha'Mikdash - Yoma 69a).' Chachamim gave many leniencies to avoid animosity. In the case I was asked about, the father was helping Yisre'elim. Perhaps he is not really serving idolatry. It is proper to draw him close.

Mishnah Berurah (9): We do not give titles of honor to his father. In another city where he is not known, we call him by his grandfather's name.

Kaf ha'Chayim (11): In our lands we always call by just his name (and Levi or Kohen), unless there are two such people.

Taz (1): The Rema says that we call an Asufi (we do not know who is his father) by his grandfather's name. I disagree. Perhaps the son will divorce his wife, and write 'I, Ploni ben Almoni', and Almoni is his mother's father. He is not really Ben Almoni, for lineage goes according to the father, so the Get is Pasul! Rather, we call him Ben Avraham. This is correct, for it says "Av Hamon Goyim."

Rebuttal (Eliyahu Rabah 4): The Rav who arranges the Get must investigate to write the correct name. This is why when the father is a Mumar, we write the grandfather's name. Perhaps this is like the opinion that is Machshir (see the Beis Shmuel below). However, this is only b'Di'eved. Also 'Ben Avraham' is Pasul, unless it says 'Avinu'!

Defense (Chachmas Shlomo): If the husband is established in the city, the Rav need not investigate his name or his father's name. Also, a Get does not need a Rav. One can divorce by himself, in front of witnesses. B'Di'eved, such a Get is Kosher.

Mishbetzos Zahav (OC 139:1): If a Get has the name of his father's father, it is Kosher b'Di'eved (see the Maharshal below), so we are not concerned if a Mumar's son uses this name. If the Get has the name of his mother's father, it is Pasul, so an Asufi may not use this name. If also the grandfather is a Mumar, perhaps one should not call him in the name of his great grandfather, for such a Get would be Pasul. 'Grandchildren are like children' does not apply to great grandchildren.

Rema (ibid.): The same applies if we are concerned for animosity of his father.

Gra (8): We give leniencies to prevent animosity. Kohanim were called by the name of Alexander Mukdan for this reason (Yosifun 5).

Shulchan Aruch (EH 129:10): If Yosef ben Shimon changed his name and wrote Yosef ben Shmuel, it is Pasul. Some say that if she remarried, she does not leave her new husband.

Beis Shmuel (19 and Taz 15): Teshuvas ha'Rosh disqualifies even if his father's father is Shmuel. The Maharshal is Machshir.

Gra (18): The father's name is essential. If there are two men in the city named Yosef ben Shimon, neither can divorce (in the absence of the other). There is no problem if their fathers have different names.

Rema: This is only if he was established with the new name. If not, she must leave. When we write a Get for the son of a Mumar, we write it in the name of his father, even if he is called to the Torah and signs his name according to his grandfather's name. A Mumar's son should not sign on a Get.

Pischei Teshuvah (29): If the Get says 'the grandson of Ploni', it is Kosher. Perhaps this is l'Chatchilah.

Pischei Teshuvah (30): Get Pasut says that even though Maharival disqualified a Get in the name of the grandfather, and she must leave, if the witness used his grandfather's name, she need not leave. One can distinguish between the husband's father and the witness' father.