Praise be to Allah.
The scholars agree unanimously that it is permissible to eat the meat of the People of the Book, Jews and Christians, if the name of Allaah is mentioned at the time of slaughter, as Allaah says (interpretation of the meaning): “Eat not of that (meat) on which Allaah’s Name has not been pronounced (at the time of slaughtering of the animal)…” [al-An’aam 6:121]. If the person mentioned a name other than that of Allaah, such as the name of ‘Uzayr or of the Messiah, then it is not permissible to eat of it, because of the general meaning of the aayah (interpretation of the meaning): “He has forbidden you… that which is slaughtered as a sacrifice for others than Allaah.” [al-Baqarah 2:173].
It is also a condition that the meat should be slaughtered in the manner prescribed by sharee’ah. If it is known that the slaughter was not done in the proper Islamic manner, e.g., by strangulation or electric shock and so on, then it is haraam.
As for the claim that some make, that it is enough merely to mention the name of Allaah when eating, this was reported regarding some Muslims who were new in Islam. The Sahaabah (may Allaah be pleased with them) asked the Prophet (peace and blessings of Allaah be upon him) about this, saying, “O Messenger of Allaah, some people who are new in Islam brought us some meat, and we do not know whether they mentioned the name of Allaah over it or not.” The Prophet (peace and blessings of Allaah be upon him) said: “Say the name of Allaah over it and eat it.”(Reported by al-Bukhaari). The command should be understood as meaning that one should be on the safe side, provided that one does not know beforehand that the meat is not slaughtered properly. And Allaah knows best.