Muddathir
The epithet appears in the opening verse of Surah Al-Muddathir (74:1) in the Quran.
Both relate to being covered or wrapped, but they appear in different surahs and contexts; Muddathir is 'the cloaked one' addressed in Surah 74, while Muzzammil appears in Surah 73.
Yes. It is used by some families seeking a direct Quranic name, though it remains uncommon and is traditionally masculine.
Yes. Common transliterations include Muddathir, Mudathir, and Al-Muddathir, reflecting attempts to render the Arabic letters and doubled consonant.
The term itself is an epithet in the Quran addressed to the Prophet; it is not primarily known as the name of a Sahabi. The primary attestations are Quranic.