Is it permissible to speak the intention out loud for example when I want to slaughter a sacrifice on behalf of my deceased father and I say, “O Allaah, it is the udhiyah for my father So and so,” or is it sufficient simply to do the deed without saying anything out loud?.
The seat of the intention is the heart, and whatever a person intends in his heart is sufficient. He should not speak the intention out loud, rather he should say Bismillaah and Allaahu akbar when slaughtering it, because it was proven in al-Saheehayn that Anas (may Allaah be pleased with him) said: “The Prophet (peace and blessings of Allaah be upon him) slaughtered two rams with his own hand, and he said Bismillaah and Allaahu akbar.” Narrated by al-Bukhaari, 7/130, no. 5554; Muslim, 3/1556, no. 1966; Ahmad, 3/115.
There is nothing wrong with you saying, “O Allaah, this is a sacrifice on behalf of my father.” This does not mean that you are speaking the intention out loud.
And Allaah is the Source of strength.