Praise be to Allah.
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 Allahu akbar when slaughtering it, because it was proven in al-Saheehayn that Anas (may Allah be pleased with him) said: “The Prophet (peace and blessings of Allah be upon him) slaughtered two rams with his own hand, and he said Bismillaah and Allahu 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 Allah, this is a sacrifice on behalf of my father.” This does not mean that you are speaking the intention out loud.
And Allah is the Source of strength.