Answer: A.      A person who was conceived through artificial insemination from a Jew is called up to the Torah by his mother’s father’s name. B.      A person who was conceived through artificial insemination from a non-Jew should be called up to the Torah only by his name, but if this will cause him embarrassment, he should be called up as the son of Avrohom Ovinu, and if this also causes him embarrassment, then he should also be called up by the name of his mother’ father. C.      If a man converted together with his father, he should nevertheless be called up to the Torah as the ‘son of Avrohom Ovinu,’ but if this causes embarrassment he can be called up as the son of his father who has also converted. D.      If a person was not born Jewish, but was adopted and converted to Judaism, he should also be called up to the Torah as the son of Avrohom Ovinu, but if necessary, he can be called up under the name of his adoptive father.Sources: So according to the opinion of the Taz, he should certainly not be called up to the Torah by his maternal grandfather’s name, as this could lead to mistaken identity and therefore inaccuracy in marriage and divorce contracts. Truthfully his father’s name according to Halocho is Avrohom, so that is how he should be called to the Torah, since he certainly descends from Avrohom, as is the case with a righteous convert.Similarly the Machatzis haShekel, (another commentator) ibid ,”if he writes using his maternal grandfather’s name, it it certainly invalid”, since in the case of a divorce, there is concern that he will use that name, (which is actually incorrect,) and thus he should not be called up to the Torah using that name.The commentator Eliyah Rabba, was not concerned that the person whose father’s name is unknown would use his maternal grandfather’s name in marriage and divorce contracts, as was the Taz, because “the Rabbi should research the father’s name, and in his research he will discover this”, and so it is clear that a mistake will not be made, and he took issue with the Taz’s assertion that the person should be called up to the Torah using the name ‘son of Avrohom’, as he states: “It is hard (to understand), that (using the name) ‘son of Avrohom’ is invalid for a divorce as the Beis Shmuel writes, if he didn’t write Ovinu,” that is to say, there is a concern that if the person is called to the Torah using the name ‘son of Avrohom’, that name will also be used in the event of divorce, and according to the Beis Shmuel that invalidates the divorce. The commentary Shaarey Efroim concurs with this opinion, and so does the Be’er Sarim, who writes: “in my humble opinion, it is highly unlikely that a rabbi who is arranging a divorce would base himself only on the name used to call the person to the Torah, for he needs to carry out thorough research on the names, as is known.”However, in the glosses of the Chochmas Shlomo, (Shulchan Oruch,) the difficulties presented by the Taz regarding the case of divorce where the rabbi involved must research the father’s name are refuted, for two reasons: “One, the rabbi need only research the name of the man getting the divorce and his father’s name if it is not known in the city, and he need not be more exacting than that. Thus, here too, if he is regularly called up to the Torah using the name ‘son of Avrohom’, it it considered as if that is his father’s name, and one need not be more exacting than that. Furthermore, it is not always necessary that a rabbi be involved in a divorce, for if he divorced his wife by himself in front of witnesses, and wrote it out in his handwriting, had the witnesses sign and gave it to his wife, she is not divorced in retrospect. And thus there is concern that she will go and marry someone else…” There is much further discussion in the responsa of various Halachic authorities.