Bukhari

Hadith Commentary:
Regarding adopting the kunyah (patronymic) of Abu al-Qasim, Imam Malik rahimahullah says that during the lifetime of the Prophet sallallahu alayhi wa sallam, this act was impermissible.
Some have considered this prohibition to be of a discouraging (tanzihi) nature.
Some have said that it is prohibited to adopt the kunyah of Abu al-Qasim together with the names Muhammad or Ahmad.
The preferred opinion is that of Imam Malik rahimahullah.

Hadith Commentary:
➊
It is understood from the context of the hadith that the Messenger of Allah (sallallahu alayhi wa sallam) was called Abu al-Qasim because he was the one who distributed wealth and possessions among the people. Although his son’s name was also Qasim, the Prophet (sallallahu alayhi wa sallam) did not mention this as the reason for his kunya (honorific title).

➋
This hadith shows that the Ansari was prohibited from naming his child Qasim, even though the Messenger of Allah’s (sallallahu alayhi wa sallam) name was not Qasim, but rather his kunya was Abu al-Qasim. The reason for this prohibition is that if a child is named Qasim, then his father would be called Abu al-Qasim.
On this basis, the father’s kunya would resemble that of the Messenger of Allah (sallallahu alayhi wa sallam). This was to avoid confusion and ambiguity.

➌
It should be noted that the prohibition of adopting the name or kunya was limited to the lifetime of the Messenger of Allah (sallallahu alayhi wa sallam).
Now, there is no fear of any kind of confusion or ambiguity, therefore both are permissible.

➍
The purpose of Imam Bukhari (rahimahullah) is that the attribution of khums (one-fifth of war booty) to the Messenger of Allah (sallallahu alayhi wa sallam) is in the sense that he was the distributor of it, not its owner.
Imam Bukhari (rahimahullah) has established his point by showing that the Prophet (sallallahu alayhi wa sallam) adopted the name Qasim (distributor).
The Giver is Allah, the Exalted; from this it is understood that the Messenger of Allah (sallallahu alayhi wa sallam) was not the owner of anything.
And Allah knows best.

Hadith Commentary:
Imam Bukhari rahimahullah strengthened the position through the narration of Imam Sufyan Thawri rahimahullah that the Ansari wanted to name his son Qasim, so that people would call him Abu’l-Qasim. However, the Ansar opposed this, and the Prophet sallallahu alayhi wa sallam praised their action. In this matter, the narrators have differed from Shu’bah. As has been mentioned above in the narration of Abu’l-Walid, he stated that the Ansari wanted to name him Muhammad.

Shaykh Ibn Hajar said: “Bukhari has mentioned the difference regarding Shu’bah—whether the Ansari intended to name his son Muhammad or Qasim—and he indicated a preference that he intended to name him Qasim, based on the narration of Sufyan, that is, al-Thawri, from al-A’mash, that he named him Qasim. This is also preferred from the perspective of meaning, because the objection from the Ansar only occurred in the case where, by naming his son Qasim, it would result in his being called Abu’l-Qasim.” (Hashiyah Bukhari)

That is, Imam Bukhari rahimahullah has mentioned the difference regarding Shu’bah on this issue—whether the Ansari wanted to name him Qasim or Muhammad—and he indicated a preference that he wanted to name him Qasim. From the perspective of meaning as well, this is preferred; the objection of the Ansar was for this very reason: that by naming the child Qasim, he would wish to be called Abu’l-Qasim.

Hadith Commentary:
➊
Imam Bukhari rahimahullah has cited the aforementioned narration to strengthen the view that the Ansari wanted to name his son Qasim so that people would refer to him with the kunyah (patronymic) Abu al-Qasim, but the Ansar opposed this, and the Messenger of Allah sallallahu alayhi wa sallam praised this conduct.
In some narrations, it is mentioned that the Ansari wanted to name his child Muhammad, but this narration is less preferred.
In any case, this prohibition was limited only to the lifetime of the Messenger of Allah sallallahu alayhi wa sallam.
➋
There is a difference of opinion regarding whether, in the case of khums (one-fifth of war booty), the Messenger of Allah sallallahu alayhi wa sallam was the owner of his share or merely the distributor. Imam Bukhari rahimahullah holds the view that the Messenger of Allah sallallahu alayhi wa sallam was not its owner, but rather its distribution was his responsibility.

Hadith Commentary: Benefits and Issues: From this hadith, it is understood that Abu al-Qasim (sallallahu alayhi wa sallam) was such that whatever he received from Allah Almighty—whether it was knowledge and virtue or wealth and riches—he would distribute it among the people. No one else possessed this quality to such a perfect degree; therefore, it is not appropriate to name someone "Qasim," so that his father would not be called "Abu al-Qasim." From this, another reason for not adopting this kunyah (patronymic) is derived. According to this reasoning, even now, adopting this kunyah does not seem appropriate. However, in his (sallallahu alayhi wa sallam) era, if someone was named Qasim, the mind could be drawn towards him (sallallahu alayhi wa sallam), but now that possibility no longer remains. Therefore, there is no harm in adopting this kunyah.