General Dought & clear, - * Removing the word ibn (“son of”) from the chain of lineage

This is Fathima XXX and I am living in the United States of America. I am expecting and we are hoping to name the Child as Hajar (name of wife of Prophet Ibrahim alai).
I was studying on the rules of naming a child according to Islam and confused how it should be mentioned in the Birth Certificate and legal documents.
Should it be Name of the child and Name of the father Eg: Hajar XXX or it should be Like e.g: Hajar binth XXX, daughter of … mentioned in the birth certificate which will be in childs official and legal documents for First, Middle and last name?
It'll be a great help if you could explain how the name should mentioned in the birth certificate, legal documents and called by parents.
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Praise be to Allah
What is customary in the Arabic language and the traditions of the Muslims is to include the word ibn (“son of”) between the name of a man and the name of his father, and to include the word bint (“daughter of”) between the name of a woman and the name of her father.
Shaykh Bakr Abu Zayd (may Allah have mercy on him) said in Mu‘jam al-Manaahi al-Lafziyyah(p. 479-480):
With regard to names such as “Muhammad Ahmad” and the like, in which the first name is refers to the individual (the son) and the second refers to the name of his father – in other words, dropping the word “ibn” between the names of two different humans.
What is customary in the Arabic language, which is confirmed by the texts of sharee‘ah is to keep the word ibn in the context of writing the lineage, both when speaking and when writing. It was not known at the beginning of Islam, or in any of the records of Islam, or the books of biography and the lives of prominent Muslim figures, that this word was ever omitted at all. This omission is due to the influence of the non-Arabs, and the west after them. The Arabian Peninsula was free of this problem until there happened what happened of people coming from all over the world, with all that they brought of the influences of non-Arabic languages, innovations, and different troubles and problems, which includes their tampering with names by dropping the word ibn. I never thought this would happen in the land of an-Najd, but Allah decrees whatever He wills.
From my experience, when I was appointed to the judiciary in al-Madinah al-Munawwarah – blessings and peace of Allah be upon its inhabitant – from 1388 to 1400 AH, I did not approve of any name being written in any record without it including the word ibn. A man who had a case in court agreed with me. I said to him: Tell me the full name of the Prophet (blessings and peace of Allah be upon him) and he said: His name is Muhammad ibn ‘Abdullah. I said to him: Why did you not say Muhammad ‘Abdullah? Have you ever heard anyone in this world who says that? Blessed is he who follows his example and follows in his footsteps, blessings and peace of Allah be upon him. And he appreciated my advice.
This is from a shar‘i point of view. From a grammatical point of view, if there is someone called Ahmad, and his father’s name is Muhammad, and his grandfather’s name is Hasan, so you call him Ahmad Muhammad Hasan, and put it in a sentence as subject or object, you will not be able to pronounce it properly (in terms of case endings in classical Arabic) or discuss it from a grammatical point of view, because the words are put together in a manner that is not acceptable according to the rules of the Arabic language. There was a lengthy discussion inMajallat Majma‘ al-Lughah al-‘Arabiyyah[Journal of the Arabic Language Council] in Egypt, and none of them came up with a valid answer (with regard to how such a name is to be pronounced or written with vowels), apart from the comment of al-‘Allaamah ash-Shaykh ‘Abd ar-Rahmaan Taaj (may Allah have mercy on him) who said that this way of putting them together is not Arabic, so it cannot be subject to Arabic grammar, because what may be subject to Arabic grammar is a phrase that is soundly put together (according to the rules of the Arabic language). So one should say “Ahmad ibn Muhammad ibn Hasan”, and not try to justify the introduction of non-Arabic ways of speaking. We should keep away from resembling the non-Arabs because that is something that we are forbidden to do, for outward resemblance is indicative of an inclination towards them in one’s heart.“So said the people before them words of similar import. Their hearts are alike” [al-Baqarah 2:118].
Inal-Eedaah wa’t-Tabyeen lima Waqa‘a fihi al-Aktharoona min Mushaabahat al-Mushrikeenby Shaykh Hammood ibn ‘Abdullah at-Tuwaijri, there is an important lengthy discussion concerning that. And Allah knows best. End quote.
The Shaykh also said in his bookTasmiyat al-Mawlood(p. 5):
The necessity of keeping the word ibn between the names when speaking of lineage:
Here I will refer to an important historical point, which is that keeping the word ibn between the name of the son and that of his father, for example, was something known to all nations, and they did not know any other way, then because of the phenomenon of infant adoption in Europe, the one who adopted a child would differentiate between the son of his own loin, whom he would call So-and-so the son of So-and-so, and his adopted son, whom he would call “So-and-so So-and-so”, dropping the word “son of”. Then the word was dropped in all cases, and this practice also spread to the Muslims in the fourteenth century AH, so that they began to say, for example, “Muhammad ‘Abdullah”!
This is a new and foreign practice that was unknown to the Arabs and it is not in harmony with their language. So it cannot be subjected to the grammatical rules of Arabic. Has the world ever heard of anyone who mentions the lineage of the Prophet (blessings and peace of Allah be upon him) and says: “Muhammad ‘Abdullah”? If anyone were to say that, he would be rebuked and disciplined, so why do we divert from following in the footsteps of the Prophet (blessings and peace of Allah be upon him), when his way is more guided and more fair and just? Look at this dropping of this word, and how it has led to confusion in cases where a name is used by both males and females, such as Asma’ and Khaarijah. On paper it would not be clear (whether the name is male or female) unless the word “ibn” (son of) or “bint” (daughter of) is added. End quote.
So the correct form of the name is to say Hajar bint Hanas.
If that is possible, then please be to Allah.
But if the law of the land where you live does not allow that, or if this will cause problems for you or for your daughter in official papers, or lead to other consequences, then there is nothing wrong with you dropping the word “bint” from her name.
The primary purpose of that is to distinguish people from one another and to know lineages. If that purpose is achieved, then this is what you want, especially if that is widespread among people and has become their custom and habit, even if the way in which names are put together is not what is ideal and more appropriate in terms of the Arabic language and the traditions of the Muslims. This applies if it is not possible to follow what is ideal.
And Allah knows best.