What is the ruling on writing the name of the pilgrim, the year of his pilgrimage, and "he performed the Hajj to the Sacred House of Allah" on his house after he has completed the obligation, and is that permissible?

This act is unlawful and involves a desire for people to know about one's good deeds. However, if the original intention of the Hajj was purely for the sake of Allah Almighty, and then he wrote what was mentioned on his house for the sake of reputation, his act is not invalidated. This is because the scholarly disagreement was concerning the intention of showing off (riya') or seeking reputation (sum'ah) during the act. Imam Ahmad and Ibn Jarir al-Tabari preferred the view that the act is not invalidated by this, and the Muslim is rewarded for his initial intention. This is what was narrated from Al-Hasan Al-Basri and others. Evidence is also drawn from Abu Dawud's hadith from 'Ata' Al-Khurasani: that the fighting of a Muslim is martyrdom if his original intent was for the word of Allah to be supreme. Ibn Jarir mentioned that this difference applies to interconnected acts, such as acts of worship. As for acts that are not interconnected, such as dhikr (remembrance of Allah) and spending money, they are cut off by a sudden intention of riya' and require a renewal of intention. It is advised not to undertake this action, for the principle is that it is desirable to conceal obedience unless there is a strong benefit in making it public.