In accordance with the Qur’an and the sunnah, it is also obligatory to invoke blessings on the Prophet şallAllāhu álayhi wa sallam to elevate his status and pay glorious tribute to the greatest benefactor of humanity. Whenever the Prophet’s şallAllāhu álayhi wa sallam name is pronounced, it is compulsory to invoke blessings on him, because this is the sunnah of Almighty Allah, Prophet Adam alaihis salam, His angels and the commandment of His beloved Prophet şallAllāhu álayhi wa sallam. The Prophet şallAllāhu álayhi wa sallam himself condemned those who do not invoke blessings upon him. The reason is that Allah has raised the remembrance of his beloved Prophet şallAllāhu álayhi wa sallam and none has the authority to lessen it:

The miserly is he, before whom I am mentioned and he does not invoke blessings on me.^[1]
Verily the most miserly amongst people is he, before whom I am mentioned and he does not invoke blessings on me.^[2]
Let his nose be smeared with dust, in whose presence I am mentioned, and he does not invoke blessings upon me.^[3]

The Prophet şallAllāhu álayhi wa sallam called him astray who does not invoke blessings upon him. It is stated as follows:
He who forgets (abandons) to invoke blessings on me, misses the road (leading) to Paradise.^[4]

Abu Hurayrah rađiyAllāhu ánhu also reported that the Prophet şallAllāhu álayhi wa sallam said:If people sit in an assembly in which they do not remember Allah nor invoke a blessing on their Prophet şallAllāhu álayhi wa sallam, it will be a cause of grief for them (on the Day of Judgment).[5]

References:
1. Tirmidhi, al-Jami‘-us-saheeh, b. of da‘wat (supplications) ch.101, (5: 551 # 3546).
2. ‘Ala’-ud-Din ‘Ali, Kanz-ul-‘ummal, (1: 489 # 2146).
3. Tirmidhi, al-Jami‘-us-saheh, b. of da‘wat (supplications) ch.101, (5: 550 # 3545).
4. Ibn Majah, Sunan, b. of iqamat-us-salat was-sunnah fiha (establishing prayer and its sunnahs) ch. 25 (1: 294 # 908); Ahmad bin Husayn Bayhaqi, Sunan-ul-kubra, 9:286.
5. Narrated by Tirmidhi in his al-Jami‘-us-saheeh, b. of dua (supplication) ch.8 (5: 461 # 3380).