My questions is about the name of the surahs: who decided to name them and how it is happened?

Question
Salam aleykum wa rahmatullahee wa barakatuhu,
First of all,May Allah reward you for your great work on about tajweed. My questions is about the name of the surahs: who decided to name them and how it is happened? Barakallahufeekum

Answer
Wa alaikum assalaam wa rahmatullahi wa barakatuh,
Jazakum Allahu khairan for your kind dua', may Allah reward you and all the questioners greatly.
The names of the different surahs are not part of the revelation, and even some of the surahs have more than one accepted name.
For example: Surah Al-Faatihah is also called al-Mathaanee, Umm Al-Kitaab, al-Hamd, to name a few. 
Surah At-Tawbah is also called surah Baraa'ah, Surah Ghaafir is also called Al-Mu'min.  These are examples and there are others.  Most of  the surahs of the Qur'an have agreed upon names and these names were either names given by the Prophet, peace and blessings of Allah upon him, or used by Sahaabah or those after them.    
Any of the accepted names can be used, and in fact different printings of the Qur'an use different names for some of the surahs.   Many times in the old literature written by early scholars, we can find the other accepted names being used.  

Wa feekum Al-Barakah.
Wa assalaam alaikum wa rahmatlulah.