Is it permissible for him to call his daughter an-Naazi‘aat?

Firstly: 

Allah, may He be glorified and exalted, says (interpretation of the meaning):

“By those (angels) who pull out (the souls of the disbelievers and the wicked) with great violence;

By those (angels) who gently take out (the souls of the believers);

And by those that swim along (i.e. angels or planets in their orbits, etc.);

And by those that press forward as in a race (i.e. the angels or stars or the horses, etc.);

And by those angels who arrange to do the Commands of their Lord, (so verily, you disbelievers will be called to account)”

[an-Naazi‘aat 79:1-5]. 

All of these are angels of the Most Merciful, may He be glorified and exalted; each of them does the actions that he is appointed to do. 

Those who pull out (an-Naazi‘aat) with great violence are the angels, when they take the souls of the sons of Adam. In some cases, the soul is taken out violently and forcefully, and in other cases it is taken out gently and easily; This is referred to in the words “By those (angels) who gently take out (the souls of the believers)” (v. 2). 

Tafseer Ibn Katheer, 8/312 

It is not appropriate to call a daughter by any of these names, because these are names and attributes that are ascribed to the angels according to what they do of various tasks. They are given these names, each according to the type of deed he does, just as in this life we may call people doctors, engineers or accountants; these titles are not given to people except for the work that they do. For one who does not hold such a position and has not been appointed to do this task by his Lord, he cannot be called by this name, even if he is an angel, let alone a human being. 

Secondly: 

It is not permissible to call daughters by names or titles of honourable angels, because that is an imitation of the mushrikeen, of whom Allah says (interpretation of the meaning):

“And they make the angels who themselves are slaves to the Most Beneficent (Allah) females. Did they witness their creation? Their evidence will be recorded, and they will be questioned”

[az-Zukhruf 43:19]

“H as then your Lord (O pagans of Makkah) preferred for you sons, and taken for Himself from among the angels daughters. Verily! You utter an awful saying, indeed”

[al-Isra’ 17:40]. 

Shaykh Bakr Abu Zayd (may Allah have mercy on him) said: With regard to calling women by the names of angels, what appears to be the case is that it is haraam, because it is an imitation of the mushrikeen who described the angels as daughters of Allah, exalted be Allah far above what they say.

End quote from Mu‘jam al-Manaahi al-Lafziyyah, p. 565 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on) was asked: 

What is the ruling on calling a girl Malaak (angel)? 

He replied: Malaak is the singular of Malaa’ik; this name cannot be given to a girl. This is also a kind of agreement with the action of the disbelievers who called the Angels the daughters of Allah: “And they make the angels who themselves are slaves to the Most Beneficent (Allah) females” [az-Zukhruf 43:19]. This meaning also indicates that it is not allowed.

End quote. Thamaraat at-Tadween min Masaa’il Ibn ‘Uthaymeen, p. 128 

Thirdly: 

Among the names that are good – of which there are many, praise be to Allah – there are sufficient names, and we have no need of these names concerning which the least that may be said is that using them is dubious. 

Ibn ‘Uthaymeen said: 

I dislike calling one’s daughter Milaak or Malaak (meaning angel), and I say: Are there too few names for him? There are thousands upon thousands of other names. Perhaps he has only this daughter; there are many names that he could take from the names of the women among the Sahaabah (may Allah be pleased with them) and the names of women in his city. As for choosing such names, the least of what we may say concerning them is that there is some doubt about this choice. In that case we say: leave that which makes you doubt for that which does not make you doubt. There are many names, praise be to Allah.

End quote from al-Liqa’ ash-Shahri, 1/184 

Fourthly: 

This name is not known among people, and its strangeness may cause people to talk and ask questions and make fun of these names, and so on, as many of the common folk tend to do. 

The fact that an-Naazi‘aat is the name of one of the soorahs of the Qur’an does not mean that it is Islamically prescribed to use this as a name for people. For example, al-Baqarah (the Cow), an-Nahl (the Bee), an-Naml (the Ant) and al-‘Ankaboot (the Spider) are all names of soorahs in the Qur’an, but that does not justify using these as names for people; rather some of the scholars have stated that it is makrooh to give people names of soorahs of the Qur’an. 

See also the answer to question no. 7180 and 82786

And Allah knows best.