The place of the intention is in the heart. Thus, what is intended in the heart is sufficient and there is no need to utter the intention verbally. Rather, one has to say ("Bismillah [In the Name of Allah]") and Takbir ("Allahu Akbar [Allah is the Greatest]") when slaughtering. This is based on the Hadith recorded in the Two Sahih (authentic) Books of Hadith (i.e. Al-Bukhari and Muslim) on the authority of
Anas (may Allah be pleased with him), who said:
The Prophet (peace be upon him) sacrificed two rams. He slaughtered them himself; he called the Name of Allah and said "Allahu Akbar".
(Part No. 11; Page No. 417)
However, it is unobjectionable to say:
'O Allah, this is an Ud-hiyah on behalf of my father,' which does not fall under uttering the intention.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.