Is it obligatory for one who slaughters on behalf of another to mention that person's name when saying the name of Allah and slaughtering?

The questioner : In this same partnership, they have the sacrificial animals, so they appointed people to do it, but is it obligatory for them, when slaughtering each sacrifice or sacrificial animal, to say, "This is for so-and-so"?

The Shaykh : For me, for example, or for so-and-so; that is better.

The questioner : That is better, but when they bring them and slaughter them without mentioning the names, or ...?

The Shaykh : It is permissible, yes, it is their agency and their intentions.

The questioner : Because the brothers are now in a difficult situation; they believe that they must slaughter the sacrificial animals again because they did not mention the names ...

The Shaykh : What was in their intention?

The questioner : Their intention was that they had taken [the animals] from individuals, and that this sacrificial animal was sent for slaughter on behalf of so-and-so, so-and-so, and so-and-so ...

The Shaykh : That is fine; since it was in their intention, there is no need to repeat the sacrifice, as long as the intention is present.