Why do we mention Prophet Muhammad’s name at the end of the prayer? Is this in Quran or just based on hadith?

This is mentioned in hadith, however, keep in mind that the Quran tells us to follow what the Prophet Muhammad (peace be upon him) taught us.

In fact, all the rules of prayer come from hadith, since the Quran told us to pray but did not explain exactly how in detail.

Therefore, it is essential to follow both the Quran and the authentic hadiths, and to make sure we are understanding both properly.

Almighty Allah knows best.