Bukhari

Hadith Commentary:
➊
In one narration, it is mentioned that the narrator of the hadith, Isma'il, asked Ibn Abi Awfa radi Allahu anhu:
"Did you see the beloved son of the Messenger of Allah sallallahu alayhi wa sallam, Ibrahim radi Allahu anhu?" He replied:
"He passed away in his childhood."
If it had been decreed for him to be a prophet after the Messenger of Allah sallallahu alayhi wa sallam, he would certainly have remained alive, but after the Messenger of Allah sallallahu alayhi wa sallam, there will be no prophet.
(Sahih al-Bukhari, al-Adab, Hadith: 6149)
➋
Imam Bukhari rahimahullah has described the attribute of Paradise that if a child dies in the age of suckling in this world, then in Paradise, arrangements are made for him to be nursed, just as was done for your son Ibrahim radi Allahu anhu.
And Allah knows best.

Hadith Commentary:
From these ahadith, it is understood that it is permissible to name children after the names of the Prophets (alayhimus salam). The Messenger of Allah (sallallahu alayhi wa sallam) himself named his beloved son after his great ancestor, Prophet Ibrahim (alayhis salam), by naming him Ibrahim. When a child was born to Abdullah bin Salam (radi Allahu anhu), he named him Yusuf and seated him in his lap. (Al-Adab Al-Mufrad, Hadith: 838) Sa'id bin Al-Musayyib (rahimahullah) states that naming after the names of the Prophets (alayhimus salam) is very beloved to him. (Fath al-Bari: 10/709)

Hadith Commentary:
From this hadith, it is also established that the children of Muslims will enter Paradise.
As for the son of the Prophet (sallallahu alayhi wa sallam), Allah bestowed an additional favor upon him: since he passed away during the period of nursing, Allah the Exalted appointed a wet nurse for him in Paradise to nurse him.
Allahumma salli ala Muhammad wa ala aali Muhammad wa barik wa sallim.

Hadith Commentary:
(1)
When the beloved child of the Messenger, Hazrat Ibrahim (radi Allahu anhu), passed away in infancy, Allah Ta’ala, in view of the greatness of His Prophet (sallallahu alayhi wa sallam), arranged for a wet nurse to breastfeed him in Paradise.
From this hadith, it is understood that the children of Muslims will be in Paradise.

(2)
Imam Bukhari (rahimahullah) narrating this hadith indicates his position that the children of Muslims will be in Paradise.
It is as if he previously had some hesitation regarding this matter, but then he expressed his inclination about it with certainty and conviction.
(Fath al-Bari: 3/311)

(3)
Imam Bukhari (rahimahullah) has also employed analogy (qiyas) in this matter: if a child can become a barrier from the Fire for his parents, then why can he himself not be veiled from the Fire?
From this, it is understood that the minor children of Muslims will be among the people of Paradise.