Reference: Fataawa al-Hajj wal-‘Umrah waz-Ziyaarah – Page 27
Question: A man made the intention to perform the Hajj for himself, whilst he has previously made the Hajj. Then he decided to change his intention for his relative whilst in ‘Arafah. So what is the ruling regarding this and is it permissible?
Response: A person, if he enters the state of ihraam for Hajj for himself, cannot change the intention after that, neither en route nor in ‘Arafah nor any other place. Rather, it is imperative he completes the Hajj for himself and does not change it for his father nor his mother and nor anyone else. Rather, the Hajj is specific for him (now) for the saying of Allaah (Subhaanahu wa Ta’aala):
{and complete Hajj and ‘Umrah for [the Sake of] Allaah}.
So, if he enters the state of ihraam for himself, it is obligatory he complete it for himself. If he enters the state of ihraam for other than himself, then it is obligatory that he completes for other than himself and does not change [the intention] once he enters the state of ihraam.
And with Allaah lies all success and may Allaah send prayers and salutations upon our Prophet ﷺ and his family and his companions.