If the one who is slaughtering a sacrifice says, “This is on behalf of So and so,” i.e., he names the one on whose behalf the sacrifice is being offered at the time of slaughter, is this uttering the intention?.
Praise be to Allaah.
This is not uttering the attention, because if the one who is offering the sacrifice says, “This is on my behalf and on behalf of my household,” he is stating what is in his heart. He has not said, “O Allah, I want to offer a sacrifice,” as would be said by the one who wants to utter his intention. Rather he is only expressing what is in his heart. The intention was already there, from the time he brought the animal, lay it down and slaughtered it, so he had already formed the intention. End quote.
Majmoo‘ Fataawa Ibn ‘Uthaymeen, 22/20