What is the ruling on changing the intention of Hajj from oneself to a relative while standing at Arafat?

If a person assumes the state of ihram for Hajj on their own behalf, they must complete it for themselves. It is not permissible for them to change their intention to perform Hajj on behalf of someone else, neither en route nor at Arafat. This is based on the Almighty's saying: (And complete the Hajj and 'Umrah for Allah). This also applies to 'Umrah.