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

Praise
be to Allah.

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.