Are the names of the surahs a matter of tawqeef?
Question

When were the names of the surahs of the Qur’an established during the period of Revelation? Is the Prophet Muhammad (blessings and peace of Allah be upon him) the one who gave the names to those surahs during his lifetime, or did the Sahaabah do that after he passed away, when they collected the Qur’an in the Mushaf during the time of ‘Umar and ‘Uthmaan?
Praise be to Allah.It is proven that the Prophet (blessings and peace of Allah be upon him) named some of the surahs of the Qur’an, such as al-Faatihah, al-Baqarah, Aal ‘Imraan and al-Kahf. 
The scholars differed as to whether the names of all the surahs of the Qur’an are proven to be from the Prophet (blessings and peace of Allah be upon him), or are some of them proven to be based on the ijtihaad of the Sahaabah (may Allah be pleased with them)? 
The majority of scholars are of the view that the names of all of the surahs of the Qur’an are proven to be from the Prophet (blessings and peace of Allah be upon him) and are the matter of Tawqeef [i.e., they can only be known through divine Revelation and sound texts of hadeeth, with no room for ijtihad]. 
Imam Ibn Jareer at-Tabari (may Allah have mercy on him) said: 
The surahs of the Qur’an have names that were given to them by the Messenger of Allah (blessings and peace of Allah be upon him). End quote. 
Jaami‘ al-Bayaan (1/100) 
Az-Zarkashi (may Allah have mercy on him) said: 
We should discuss the issue of when a surah has more than one name: is this the matter of tawqeef, or does it have to do with the stories mentioned in the surah? 
If the latter is the case, then any smart man could derive from each surah many names based on its contents, and this is unlikely. End quote. 
Al-Burhaan fi ‘Uloom al-Qur’an (1/270) 
As-Suyooti (may Allah have mercy on him) said: 
It is proven that all the names of the surahs are the matter of tawqeef, based on hadiths and reports. Were it not that I fear it would take too long, I would have explained that. End quote. 
Al-Itqaan (1/148) 
Shaykh Sulaymaan al-Bujayrami (may Allah have mercy on him) said:
The names of the surahs are the matter of tawqeef and are narrated from the Prophet (blessings and peace of Allah be upon him), because the names of the surahs, the order in which they appear, and the order of the verses – each of these three things is the matter of tawqeef and is narrated from the Prophet (blessings and peace of Allah be upon him). Jibreel (peace be upon him) told him that this is how they were in al-Lawh al-Mahfooz. End quote. 
Tuhfat al-Habeeb ‘ala Sharh al-Khateeb (2/163) 
Al-‘Allaamah at-Taahir ibn ‘Ashoor (may Allah have mercy on him) said: 
With regard to the names of the surahs, they were given to them during the period of Revelation. The purpose of naming them is so as to make it easy to refer to them and discuss their meanings. End quote. 
At-Tahreer wa’t-Tanweer (1/88) 
This is the view favoured by a number of contemporary scholars who have written about the sciences of Qur’an, such as Dr. Fahd ar-Roomi in Diraasaat fi ‘Uloom al-Qur’an (p. 118), and Dr. Ibraaheem al-Huwaymil in his paper al-Mukhtasar fi Asma’ as-Suwar, in Majallat Jaami‘at al-Imam (issue no. 30, p. 135). 
Some of the scholars are of the view that some of the names of the surahs in the Holy Qur’an were given to them by the Prophet (blessings and peace of Allah be upon him), and some of them were the result of the ijtihaad of the Sahaabah (may Allah be pleased with them). 
It says in Fataawa al-Lajnah ad-Daa’imah (4/16): 
We do not know of any text from the Messenger of Allah (blessings and peace of Allah be upon him) to suggest that he named all of the surahs, but it is narrated in some saheeh hadiths that some of them were named by the Prophet (blessings and peace of Allah be upon him), such as al-Baqarah and Aal ‘Imraan. As for the other surahs, what appears to be the case is that they were named by the Sahaabah (may Allah be pleased with them). End quote. 
This is what was deemed most likely to be correct by Dr. Muneerah as-Dawsari in her essay: Asma’ Suwar al-Qur’an al-Kareem wa Fadaa’iluha. 
And Allah knows best.