Bukhari

Hadith Commentary:
The intended meaning is the person who considers such an act to be permissible, or it is for the purpose of severe warning, or by "kufr" here is meant ingratitude (unthankfulness).
And Allah knows best.

Hadith Commentary:
➊
It is understood from this hadith that it is forbidden (haram) to claim ownership of something that does not belong to a person, whether it pertains to wealth and possessions, or to knowledge and virtue, or to lineage and ancestry. Thus, some people attribute themselves to a group other than their own tribe; they too fall under the warning mentioned here. For example, some people ascribe themselves to the Sayyids so that they may be respected in the eyes of the public. They are included in the purview of this hadith.

➋
By "kufr" here is meant ingratitude (kufran-e-ni‘mah), or it means that whoever considers it lawful (halal) to attribute himself to someone else is truly a disbeliever (kafir), or the mentioned expression is for the purpose of rebuke and reprimand. If he repents, then this sin will be forgiven.

➌
Hafiz Ibn Hajar rahimahullah writes:
When it has been established that the people of Yemen are the descendants of Hazrat Isma‘il alayhis salam, then it is not correct for them to attribute themselves to anyone else. This is the meaning that Imam Bukhari rahimahullah has derived from this hadith.
(Fath al-Bari: 6/660)

Hadith Commentary:
Vocabulary of the Hadith:
(1)
ادَّعَى:
To claim.
(2)
عَادَ عليه:
Has the same meaning as بَاءَ and رَجَعَ — to return, to go back, to come back.

Benefits and Issues:
(1)
To deny one’s real lineage and claim to be the son of someone else is an extremely criminal act... and this is kufr duna kufr (disbelief less than outright disbelief) which does not expel one from the fold of Islam, and this act will be considered kufr. If someone does this due to some interpretation or necessity, then this will be considered ingratitude for blessings (kufran al-ni‘mah), just as the Prophet (sallallahu alayhi wa sallam) said regarding women: “YAKFURNA AL-ASHIR” — they are ungrateful and unappreciative towards their husbands. In the same way, this person is ungrateful for the rights of Allah and his father.

(2)
If someone knowingly claims ownership of something that is not his, then this is a lie and a usurpation of another’s property, which is contrary to the character of a true and complete believer. That is why the Prophet (sallallahu alayhi wa sallam) said: “He is not from among us.” Just as regarding the son of Nuh (alayhis salam), Allah the Exalted said:
﴿إِنَّهُ لَيْسَ مِنْ أَهْلِكَ﴾ “Indeed, he is not of your family.”
That is, his way, conduct, behavior, and dealings are not those of the Muslims, and this is such a fault and an open sin for which the punishment is Hell, unless the person repents from it or Allah the Exalted forgives him.

Benefits and Issues:

➊
The meaning of "He is not one of us"
is that this action of his is not the action of Muslims, and his faith is not complete.

➋
The meaning of "He should make his abode in Hell"
is that he should be certain that he will go to Hell; therefore, to save himself, he should avoid this sin.
And if this sin has been committed, then he should return the right to its rightful owner, repent, and thus save himself from Hell.

➌
The Prophetic statement is:
"Whoever testifies that there is no deity except Allah and that Muhammad (sallallahu alayhi wa sallam) is the Messenger of Allah, Allah makes the (Hell) Fire forbidden for him." (Sahih Muslim, Kitab al-Iman, Chapter: The evidence that whoever dies upon Tawhid will definitely enter Paradise, Hadith: 26)
This does not mean that he will not be punished for his sins; rather, it means that he will not suffer the punishment of remaining in Hell forever.