The eminent Muslim scholar, Sheikh Yusuf Al-Qaradawi, states: “Some scholars are of the view that although the Name of Allah must be mentioned, it is not necessary to mention it at the time of slaughtering the animal; one can mention it at the time of eating, since in that case it cannot be held that it was eaten without mentioning the Name of Allah over it.
Al-Bukhari narrated the following Hadith on the authority of `A’ishah, may Allah be pleased with her: “Some people who had recently embraced Islam said to the Prophet, peace and blessings be upon him, ‘People bring us meat and we do not know whether they have mentioned the Name of Allah when slaughtering it or not. Shall we eat of it or not?’ The Prophet, peace and blessings be upon him, replied, ‘Mention the Name of Allah (over it) and eat.’”
Also, it is reported that the Prophet, peace and blessings be upon him, used to say the following Du`a’ (supplication) when he began to eat or drink: Bismillah Ar-Rahman Ar-Raheem, (In the Name of Allah, Most Gracious, Most Merciful), coupled with a Du`a’ such as: Allahumma barik lana fima razaqtana wa qina `adhaban-nar (Our Lord, bless us in what You have provided for us and save us from the punishment of the Fire).”
In the light of the above, it becomes crystal clear that mentioning the name of Allah at the time of eating can compensate for not mentioning it at the time of slaughtering the animal.