Abu Dawud

Benefits and Issues:
The circumstances of a Muslim are, in principle, to be regarded as good and upright.
Except if some clear and explicit matter comes to light.
Therefore, one should not fall into doubt merely on the basis of suspicion or conjecture.
Deliberately omitting to say "Bismillah" while slaughtering an animal is impermissible.
However, forgetfulness is excused.
And in such a case, there should be no doubt or uncertainty regarding the permissibility of the slaughtered animal.

Hadith Commentary:
It has been established that invoking the name of Allah is for the sake of blessing, permissibility, and assistance; this is the relevance to the chapter.

Hadith Commentary:
➊
The meaning of the Companions (radi Allahu anhum ajma'in) presenting this issue was that people had recently embraced Islam and were not yet well acquainted with the rulings regarding slaughter and similar matters. It was possible that, at the time of slaughter, they might not mention the name of Allah.
The Messenger of Allah (sallallahu alayhi wa sallam) said:
“One should have a good opinion about Muslims, that they would mention the name of Allah at the time of slaughter. However, the one who uses (the meat) should himself mention the name of Allah and then eat it.”
This absolutely does not mean that if an animal was slaughtered without mentioning the name of Allah, it becomes permissible to eat it by reciting ‘Bismillah’ over it before eating.
The command of Allah, the Exalted, is:
“Do not eat (of that) upon which the name of Allah has not been mentioned (at the time of slaughter).” ()

➋
In this hadith, another manner and style of invoking Allah by means of His names is described: that at the time of slaughter and at the time of eating, the name of Allah should be mentioned. The Messenger of Allah (sallallahu alayhi wa sallam) has informed us of the goodness and blessing in this.
Imam Bukhari (rahimahullah) has narrated this hadith for this very purpose.
The intention is not to explain the rulings of slaughter.

Hadith Commentary:
The meaning is that one should have a good opinion of a Muslim, and unless it is established by evidence that the Muslim did not say "Bismillah" at the time of slaughter, or that he mentioned a name other than Allah, the meat brought or prepared by him should be considered lawful (halal).
The meaning of the hadith is not that the meat brought or prepared by polytheists (mushriks) should be considered lawful, and the jurists (fuqaha) have explicitly stated that if a polytheist butcher claims that the animal was slaughtered by a Muslim, his statement will not be accepted.
Therefore, one must exercise great caution and avoidance in taking meat from a polytheist or disbelieving butcher.

Hadith Commentary:
(1)
Imam Bukhari rahimahullah’s intent is to describe the baseless fears of those afflicted with misgivings, showing that such fears have no real standing—just as someone might refrain from eating the meat of a hunted animal merely out of suspicion that perhaps someone else hunted it, the animal escaped, and then fell into his own hands. In the presented hadith as well, such a kind of misgiving is mentioned, to which the Messenger of Allah sallallahu alayhi wa sallam gave no importance.

(2)
One should maintain a good opinion about Muslims, believing that they certainly pronounced Allah’s name at the time of slaughter. To doubt that perhaps the person did not mention Allah’s name at the time of slaughter is merely a baseless misgiving and suspicion. Such thoughts should not be entertained; rather, one should recite “Bismillah” oneself and proceed to use it. From both these narrations, it is understood that misgivings are not among those doubts from which it is necessary to abstain. As long as misgivings do not become firmly rooted and settled in the heart, there is no accountability for them.

(3)
Hafiz Ibn Hajar rahimahullah has written that this hadith is evidence for maintaining a good opinion about Muslims, and also that the affairs of Muslims are to be assumed to be in a state of completeness. This is especially the case in times when every Muslim is well acquainted with the religion of Islam. (Fath al-Bari: 4/375)

(1) The animal slaughtered by any Muslim or by someone from the People of the Book will be considered lawful (halal), and in case of doubt or suspicion, mentioning the name of Allah while eating the meat will also remove the doubt or suspicion. However, it is absolutely not permissible to eat the meat slaughtered by Sikhs, Magians (Zoroastrians), polytheists, etc.

(2) Items found in Muslim cities and markets, etc., will be considered lawful (halal) unless there is a clear evidence of their prohibition; mere suspicion does not establish the prohibition of anything. For further clarification on this issue, refer to the words of the Grand Mufti of Saudi Arabia, Shaykh Abdul Aziz bin Abdullah bin Baz rahimahullah. He states: “The meat sold in the markets of non-Islamic countries, if it is known regarding it that it is the meat of animals slaughtered by the People of the Book (Jews or Christians), then it is lawful (halal) for Muslims (until) it is known that (the animal from which the meat is taken) was slaughtered in an un-Islamic manner. This is because, according to the Qur’anic text, its original ruling is that it is lawful, therefore, in this case, the original ruling (of permissibility) stated by the Noble Qur’an will not be abandoned until there is firm evidence that necessitates its prohibition. And if that meat is from animals slaughtered by other disbelievers (besides Jews and Christians), then it is unlawful (haram) for Muslims, and due to the text and consensus (ijma‘) of the Ummah, it is impermissible to eat such meat. Such meat does not become lawful merely by mentioning the name of Allah at the time of eating.” And Allah knows best. See: (Dhakheerat al-‘Uqba Sharh Sunan al-Nasa’i: 34/51)

Benefits and Issues:
The reason for the doubt was that these new Muslims might not know the ruling that one must slaughter in the name of Allah.
So it was explained that you should not have any doubt; rather, recite "Bismillah" and eat.