Concerning the names of the surahs, Scholars agree that the names of the surahs were given to them based on revelation. This means that it is either that Almighty Allah sent Gabriel down with the names of the surahs to the Prophet who told the Companions about them or the Prophet himself was guided to name them and then revelation came in support of what he did.
The first of these two opinions is adopted by the majority of Muslim scholars who are specialized in the sciences of the Quran and it is stated by Jalal al-Din Al-Suyuti as he says:
"It has been proven that the names of the surahs have all been given by means of tawqeef (Divine guidance through revelation)". (Jalal al-Deen Al-Suyuti, Al-Itqan fi Ulum Al-Quran, vol. 1, Cairo, n.d., p. 147)
This is even proven by many hadiths mentioning the names of the surahs as we know them today. For instance, An-Nawwas ibn Sam`an narrated that he heard the Messenger of Allah saying:
"On the day of Judgment, the Quran and its people who used to stick to its teachings will be brought with Surat Al-Baqarah and Aal `Imran preceding them." (Muslim)
Abdul-Rahman ibn Yazid also narrated that he heard Ibn Masud (may Allah be pleased with him) saying that Banu Isra'eel (i.e. Surat Al-Israa'), Al-Kahf, Maryam, Taha and Al-Anbiyaa' are among the early surah that I have learnt by heart." (Al-Bukhari)
This shows that the surahs of the Quran were known by the same name during the lifetime of the Prophet and it was him who gave them the names based on revelation he received from Almighty Allah as is opined for by the majority of Muslim scholars.
Yet, there is one important point to be highlighted here, why do we hear many names of some surahs? For instance, Surat Ash-Sharh is also called Al-Inshirah and Alam Nashrah, why is that?
We have to differentiate here between what is written in the mushaf (copy of the Quran) as the name of the surah and what is being used sometime by people as a reference to the surah which could be the first words of the surah or another derivative of its name.
This obviously does not contradict the fact that the Quran is preserved and protected because the name of the surah is the same in the mushaf and no one can change it.
The other point is that there are some surahs which were given more than one name by the Prophet. Although we can use any of these names, we still prefer to use what is mentioned in the mushaf as this is the most common name among people.
To exemplify this, we quote the fact that Surat Al-Israa' was also called Bani Israel by the Prophet, Surat Al-Fatihah was called Umm Al-Quran and As-Sab` Al-Mathani, etc.
These other names of the surahs can be known by looking into specialized books, yet the same fact remains that these names were revealed to the Prophet and one of them was frequently chosen by him to refer to the surah.
Part of the accuracy of Muslims is that they narrated the other names and they can still be alternatively used to refer to the surah with a recommendation to use the one that is kept in the mushaf as being the most common and the easiest one.
