Question

Who was the author of the Manusmriti?

Answer

So who was this narrator who wrote the Manusmriti?

It depends on whether you are looking for the traditional answer or an academic (non-faith) scholarly opinion. Based on your citing the example of Vyasa/Ganesha for the Mahabharata, it appears you are looking for the former.

In that case, the narrator of the Manu-Smriti is Bhrigu Maharshi.

The last verse of the text reads:

इत्येतन् मानवं शास्त्रं भृगुप्रोक्तं पठन् द्विजः ।
भवत्याचारवान्नित्यं यथेष्टां प्राप्नुयाद् गतिम् ॥ १२-१२६ ॥ ityetan mānavaṃ śāstraṃ bhṛguproktaṃ paṭhan dvijaḥ |
bhavatyācāravānnityaṃ yatheṣṭāṃ prāpnuyād gatim || 12-126 ||

Bhṛguproktaṃ means 'spoken by Bhṛgu'

Additionally, if you look at the ending colophon of every chapter in the Manu-Smriti, it says:

iti mānave dharmaśāstre bhṛgu-proktāyāṃ saṃhitāyām

meaning that the Mānava dharmaśāstra is from the Saṃhitā spoken by Bhṛgu.

Here's an example from the end of the first chapter (version edited by Mahamahopadhyaya Ganganatha Jha)

enter image description here

To be clear, the Manu Smriti is a smaller portion of the Bhrigu Samhita that is authored by Bhrigu. It is not clear if Bhrigu quotes Manu verbatim or whether he is paraphrasing / summarizing / rewording the content of what Manu spoke. This is not very different from the Bhagavad Gita (words of Krishna) appearing in the Mahabharata (written by Vyasa).

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