Is there a Surah in the Qur'an named Al-Munajat?

There is no Surah in the Quran called "Surat Al-Munajat" (The Chapter of Secret Counsel). Rather, there is the verse of secret counsel, which is verse 12 of Surat Al-Mujadilah (The Chapter of the Pleading Woman): "O you who have believed, when you [wish to] secretly consult the Messenger, present before your private consultation [a charity]."

It was narrated from Ali (may Allah be pleased with him) that he said: "There is a verse in the Book of Allah that no one before me acted upon, nor will anyone after me act upon it." He was the only one who secretly consulted the Messenger after its revelation, and he presented a dinar and gave it in charity. Then, the dispensation was revealed, lifting the obligation of charity.

Qatadah also mentioned that this verse was revealed because of the people's excessive questioning of the Messenger of Allah (peace be upon him). So, no one could secretly consult him except by presenting a charity. When this became difficult for them, the dispensation was revealed.