Who is the first one who named the chapters of the Quran?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

The scholars differed in opinion whether or not the naming of the chapters of the Quran was determined by revelation. As-Sayooti said: 'It is confirmed that the names of the chapters of the Quran are determined by Prophetic narrations and statements of the companions .'

What As-Sayooti said is confirmed in some Prophetic narrations. The Prophet said: "The Quran and the people who used to act upon it will be brought on the Day of Judgement, and at its beginning will be the chapter of Al-Baqarah (the Cow) and Aal-'Imraan (the family of Imraan)." [Muslim, At-Tirmithi, and Ahmad]

Therefore, the first person who named the chapters of the Quran is the Prophet (through revelation).

Allaah Knows best.