I was never given a Hebrew name. My father is a non-Jew and my mother is a Jew. I understand that the last part of the Hebrew name is the first part of the father's Hebrew name. What would the method be for determining my Hebrew name be?
[Administrator's note: A related question is found at http://www.jewishvaluesonline.org/question.php?id=298.]
A person’s name is a way of distinguishing him/her from others, of identifying the individual as distinct from anyone else. As such, a name must have distinctive features so that thereby we are able to, with few exceptions, identify one individual as separate from another. It is thus important that within the mechanism of a name we are able to narrow down, to a great extent, the individual to whom we are referring.
Within the Jewish world, this is accomplished, generally, through the use of an individual’s personal name with a further reference to a parent. In most cases, the parent mentioned is the father so a full Hebrew name would generally be one’s individual personal name with the further mention that the individual is the son or daughter of the father. When the father is not Jewish, however, this reference to the father is not applied within Jewish Law. The essence of your question is as such: what other criteria is used in the name identification of a person if the father’s name is not used, such as in a case when the father is not Jewish? (The same question may be asked when, for example, the father’s identity is not known.)
The usual custom in such cases is to follow the view of Rema, Shulchan Aruch, Orach Chaim 139:3 who states that the name of the father of the mother (i.e. the maternal grandfather) should be used instead of the father’s name. There are those, however, who disagree. See Mishneh Brura 139:10. The second option which then seems to have the most weight is to simply refer to the individual as the son or daughter of Avraham Avinu, Avraham our forefather. So in answer to your question, you have two basic options: either to refer to yourself as the son/daughter of your maternal grandfather or as the son/daughter of Avraham.
I should mention, perhaps, that there are actually also two other possibilities. As reference in a name is given to the mother in certain cases -- such as in prayers for health – the option to refer to you as the son/daughter of your mother is also presented, within the literature, as a possibility. The idea that perhaps you should just refer to yourself with one name, your personal individual one, is also found. These two latter options, however, reflect limited, minority opinions and, in the determination of your Hebrew name, it would be best if you choose one of the first two options.
If your mother is Jewish, then you are uncategorically a member of the Jewish people and would not require conversion. Historically, Jewish tradition would base your Hebrew name on that of your mother only and according to the Talmud (Babylonian Talmud, Yevamot 98a) would consider you with a father of unknown origin so his name wouldn't be included in your Hebrew name formula (for when you're called up for an aliyah to the Torah.
In modern time, I would advise you to include your father's English name if that is your preference (along with your mother's Hebrew name of course). If your father is a follower of a religion other than Judaism, it might be awkward to include his name when you're called up for an aliyah so you should consider that when making the decision.
Rabbi Blair answered this question for another situation and the answer would still be the same - as such, your Hebrew name would be Ploni ben Mother's Name. However, I, along with other rabbis, do offer the option of transliterating the father's name into Hebrew or obtaining a Hebrew equivalent to the father's English name. This is where it becomes a little complicated as well as a potential socio-political situation. The problem is defining one's jewish identity. Some will state that the father's name should not be stated at all if he is not Jewish. I think it shouldn't matter as the traditional Jewish identity is through the mother. If you have a non-Jewish mother and a Jewish father, the question of the Hebrew name is not an issue - only the Jewish identity of such progeny.
As a Reform Jew, I consider a person Jewish if one of the parents is Jewish AND the person has participated in appropriate and timely public and formal acts of indentification with the Jewish faith and people. As such, the Jewish identity is possible through either parent. Yet, I also acknowledge that within traditional Jewish law, the child is Jewish as long as the mother is Jewish. With this being noted, the questioner simply ignores his father's name in his Hebrew name. The alternative is to transliterate or translate the father's name into Hebrew and include his mother's name too - i.e. Ploni ben Thomas v'Mother. Since the questioner is Jewish according to traditional Jewish law no matter what, the father's religious identity should have no bearing on the full name. If you wish to honor your father's name, go ahead.
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