It is not prescribed to utter the intention for Hajj or for ‘Umrah
Question

If the pilgrim says “Labbayka ‘umratan (here I am for ‘Umrah)” or “Laybbayka hajjan (Here I am for Hajj)”, is that regarded as uttering the intention?.
Praise be to Allah.If a person says “Labbayka ‘umratan (Here I am for ‘Umrah)” or “Laybbayka hajjan (Here I am for Hajj)”, that does not come under the heading of forming the intention, because he formed the intention before that. Hence it is not prescribed to say, “O Allah, I am going to do ‘Umrah” or “O Allah, I am going to do Hajj.” Rather you should form the retention in your heart and recite the Tabiyah out loud. With regard to uttering the intention for actions other than Hajj or ‘Umrah, this is something which it is well known is not prescribed. It is not Sunnah for a person to say, when he wants to do wudoo’, “O Allah, I am going to do wudoo’” or “O Allah, I intend to do wudoo’”, or when he wants to pray to say “O Allah, I am going to pray” or “O Allah, I intend to pray.” None of that is prescribed. And the best guidance is the guidance of Muhammad (blessings and peace of Allah be upon him). End quote.