Giving children the names of the Prophets who are mentioned in the Holy Qur’an
Question

What is the ruling on giving children the names of the Prophets who are mentioned in the Holy Qur’an, with the intention of offering supplication for them when reciting Qur’an in prayer or in one’s daily wird (litany), in particular the verses (interpretation of the meaning):
{And remember Our servants, Ibraaheem, Ishaaq and Ya‘qoob - those of strength and [religious] vision.
Indeed, We chose them for an exclusive quality: remembrance of the home [of the Hereafter].
And indeed they are, to Us, among the chosen and outstanding} [Saad 38:45-47].
Praise be to Allah.Giving children the names of the Prophets who are mentioned in the Holy Qur’an is recommended and is Sunnah.
This is mentioned in the hadith of Anas ibn Maalik, who said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Last night a boy was born to me, and I have named him after my father Ibraaheem.” Narrated by Muslim (2315).
It was narrated that Abu Moosa said: A son was born to me and I took him to the Prophet (blessings and peace of Allah be upon him). He named him Ibraaheem and rubbed his palate with some dates (tahneek), and he prayed for blessing for him and gave him back to me. Narrated by al-Bukhaari (6198) in a chapter entitled Who named children after the Prophets. Also narrated by Muslim (2145).
It was narrated that Yoosuf ibn ‘Abdillah ibn Salaam (may Allah be pleased with him) said: The Prophet (blessings and peace of Allah be upon him) named me Yoosuf; he sat me on his lap and patted me on the head. Narrated by al-Bukhaari in al-Adab al-Mufrad (838) in a chapter entitled The names of the Prophets.; classed as saheeh by al-Haafiz Ibn Hajar in Fath al-Baari (10/578) and by al-Albaani in Saheeh al-Adab al-Mufrad.
We have an example in the Messenger of Allah (blessings and peace of Allah be upon him, as Allah, may He be exalted, says (interpretation of the meaning):
{There has certainly been for you in the Messenger of Allah an excellent example for anyone whose hope is in Allah and the Last Day and [who] remembers Allah often} [al-Ahzaab 33:21].
Ibn Katheer (may Allah have mercy on him) said:
This verse sets out an important basic principle, which is that we should follow the example of the Messenger of Allah (blessings and peace of Allah be upon him) in his words and deeds, in all situations." (Tafseer Ibn Katheer  6/391).
Reciting the supplications mentioned in the Qur’an with the intention of offering supplication is something that is prescribed in Islam. Hence it is prescribed to say Ameen after reciting al-Faatihah, because of what it contains of supplication.
Ibn Katheer (may Allah have mercy on him) said:
It is recommended (mustahabb) for the one who recites al-Faatihah to follow that by saying Ameen, which means: O Allah, answer…
Our companions and others said: That is recommended for one who is not praying, and is more emphasized in the case of one who is praying, whether he is praying alone, leading the prayer or praying behind an imam, in all situations." (Tafseer Ibn Katheer  1/144-145).
But with regard to reciting the verses that you mention in the question, which are:
{And remember Our servants, Ibraaheem, Ishaaq and Ya‘qoob - those of strength and [religious] vision.
Indeed, We chose them for an exclusive quality: remembrance of the home [of the Hereafter].
And indeed they are, to Us, among the chosen and outstanding} [Saad 38:45-47],
with the intention that it be a supplication for your children, this is not a supplication (du‘aa’). Rather in this passage Allah, may He be exalted, is telling us of the status of these Prophets (peace be upon them).
So reciting this passage with the intention that it be a supplication for your children who have these names is a kind of distorting the meanings of the Holy Qur’an, and not reflecting upon it in appropriate manner.
But if you want to offer supplication for your children, then pray for them saying: “O Allah, and make righteous for me my offspring, O Allah, my son Ibraaheem” – if your son’s name is Ibraaheem – and so on, otherwise what is the point of reciting a verse with the intention that it is for your children?
We should point out that there is no stipulation that supplication offered during the prayer should be from the Holy Qur’an; rather a person may offer during prayer whatever supplication he likes, asking for what is good.
In the hadith, ‘Abdullah ibn Mas‘ood said: When we prayed with the Prophet (blessings and peace of Allah be upon him), we used to say: Peace (as-salaam) be upon Allah from His slaves; peace be upon So-and-so and So-and-so. The Prophet (blessings and peace of Allah be upon him) said to us: “Do not say peace (as-salaam) be upon Allah, for Allah is as-Salaam; rather say: al-tahiyyaatu Lillaahi wa’s-salawaatu wa’t-tayyibaat; as-salaamu ‘alayka ayyuha’n-nabiyyu wa rahmat-Allahi wa barakaatuhu; as-salaamu ‘alayna wa ‘ala ‘ibaad-illaah is-saaliheen (All compliments, prayers and good words are due to Allah; peace be upon you, O Prophet, and the mercy of Allah and His blessings; peace be upon us and upon the righteous slaves of Allah). For if you say that, it will reach every slave of Allah in the heavens and on earth. (Then say:) Ash-hadu al-laa ilaaha ill-Allah wa ash-hadu anna Muhammadan ‘abduhu wa rasooluhu (I bear witness that there is no god worthy of worship except Allah and I bear witness that Muhammad is His slave and Messenger). Then let him choose whatever supplications he wishes.” Narrated by al-Bukhaari (835) and Muslim (402).
And Allah knows best.