Bukhari

Hadith Commentary:
During the lifetime of the Prophet (sallallahu alayhi wa sallam), calling someone by the name Abu al-Qasim would cause confusion because Abu al-Qasim was the kunyah (patronymic) of the Prophet (sallallahu alayhi wa sallam) himself.
Therefore, he (sallallahu alayhi wa sallam) forbade anyone from adopting the kunyah Abu al-Qasim so that there would be no confusion.
After him, the scholars have permitted adopting this kunyah.
‘Abdullah and ‘Abd al-Rahman are beloved names to Allah because they denote attribution to Allah, which expresses the servitude of the servant.
The subject of the chapter is explicitly mentioned in a hadith: "The most beloved names to Allah are ‘Abdullah and ‘Abd al-Rahman."

Hadith Commentary:
(1)
Imam Bukhari rahimahullah has selected a portion of a hadith in the chapter heading.
The complete hadith is as follows: The Messenger of Allah sallallahu alayhi wa sallam said:
“The most beloved names to Allah are Abdullah and Abdur-Rahman.” (Sahih Muslim, Al-Adab, Hadith: 5587(2132))
The reason for the preference of these names is that they ascribe servitude to Allah Almighty.
It is a great fortune for any person that he is always called by this lofty attribution.

(2)
The particularity of these two names is that in the Noble Qur’an, the addition of “abd” (servant) is made to “Allah” and “Ar-Rahman.”
Besides these, those names are also included which ascribe servitude to any of the names of Allah Almighty, such as Abdul-Qayyum, Abdul-Jabbar, and Abdul-Rabb, etc.
And Allah knows best.