The Surah has been so designated after the word al-muzzammil occurring in the very first verse. This is only a name and not a title of its subject matter.
The two sections of this Surah were revealed in two separate periods....
The first section (vv. 1-19) is unanimously a Makki Revelation, and this is supported both by its subject matter and by the traditions of the Hadith. As for the question, in which specific period of the life at Makkah it was revealed, it is not answered by the tradition, but the internal evidence of...