Why do Muslims add "peace be upon him" after names of important people?

Muslims add "peace be upon him" (often abbreviated as PBUH) after mentioning the names of important figures, especially the Prophet Muhammad ﷺ, as a sign of respect and reverence. This practice is rooted in the teachings of the Qur'an and the traditions of the Prophet.

In the Qur'an, Allah commands believers to bless the Prophet, stating: Lo! Allah and His angels shower blessings on the Prophet. O ye who believe! Ask blessings on him and salute him with a worthy salutation. 33:56. This verse highlights the importance of sending salutations and blessings upon the Prophet, establishing it as a significant aspect of Islamic practice.

Furthermore, hadith literature provides insight into the Prophet's ﷺ teachings regarding this practice. In one narration, it is reported that 'Abdullah said, 'Whenever we prayed behind the Prophet we used to recite (in sitting) 'Peace be on Gabriel, Michael, peace be on so and so. Once Allah's Apostle looked back at us and said, 'Allah Himself is As-Salam (Peace), and if anyone of you prays then he should say, At-Tahiyatu lil-lahi wassalawatu wat-taiyibatu. As-salamu 'alalika aiyuha-n-Nabiyu wa rahmatu-l-lahi wa barakatuhu. As-Salam alaina wa ala ibadil-lah is-salihin. (All the compliments, prayers and good things are due to Allah: peace be on you, O Prophet and Allah's mercy and blessings be on you. Peace be on us an on the true pious slaves of Allah). (If you say that, it will be for all the slaves in the heaven and the earth). Ash-hadu an la-ilaha illa-l-lahu wa ash-hadu anna Muhammadan 'abduhu wa Rasuluhu.' Sahih al-Bukhari 12:794. This narration illustrates how the Prophet ﷺ emphasized the practice of sending peace upon him and the significance of this act in prayers.

In Shia tradition, the importance of this greeting is also affirmed. As narrated in Al-Kafi, I asked abu ‘Abd Allah, recipient of divine supreme covenant, ‘What is the meaning of ‘Peace be with the Messenger of Allah (or offering him the greeting of peace)?’ The Imam said, ‘When Allah, the Most Holy, the Most High, created His Prophet... Offering of peace to him is a mention of that covenant and renewing it before Allah, so that perhaps He, the Most Majestic, the Most Gracious, will allow that peace to take place soon for all of you with all that is therein.’ Al-Kafi 111:1220. This highlights that the greeting of peace is not only a sign of respect but also a renewal of a sacred covenant with Allah.

Overall, the practice of saying "peace be upon him" serves as a reminder of the Prophet's ﷺ noble status and the respect that he commands in the hearts of Muslims.