The Standing Committee for Islamic Research and Ifta’ issued the following fatwa: The seat of the intention is the heart, and whatever a person intends in his heart is sufficient. He should not speak the intention aloud; rather he should say “Bismillah” and “Allahu Akbar” when slaughtering it, because it is reported that Anas (may Allah be pleased with him) said, “The Prophet (peace and blessings be upon him) slaughtered two rams with his own hand, and he said ‘Bismillah’ and ‘Allahu Akbar’” (Al-Bukhari and Muslim).
In addition, 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 aloud.