Intention for Hajj
Hajj is an obligation which every person owes Allah once in their lifetime. Hajj and Umrah are also an expiation for sins. Both these reasons should form part of your intention.
The Prophet ﷺ says:
“The performance of Umrah is expiation for the sins committed between it and the previous ones. And the reward for Hajj Mabrur (pilgrimage accepted by Allah) is nothing but Paradise.”(Bukhari)
Hajj is a tremendous act of worship and every act of worship pleases Allah, so the intention should also be to seek the pleasure of Allah.