Why did the Prophet PBUH name, Muhammad?
Rasullullah PBUH said:
لِي خَمْسَةُ أسْماءٍ: أنا مُحَمَّدٌ، وأَحْمَدُ وأنا الماحِي الذي يَمْحُو اللَّهُ بي الكُفْرَ، وأنا الحاشِرُ الذي يُحْشَرُ النّاسُ على قَدَمِي، وأنا العاقِبُ
“I have five names. I am Muhammad. I am Ahmad. I am al-Mahi (the effacer), by whom Allah effaces kufr. I am al-Hashir (the gatherer), before whom people are gathered. I am al-Aqib (the last).” 
Imam Ibn Hajar al-‘Asqalani stated that it is as though both these names are the most famous names of his and the name Muhammad is the most well-known between the two.  Imam al-Suyuti also stated that Muhammad is his most famous name. 
According to al-Qadhi ‘Iyadh as cited by Imam al-Suyuti, both these names Muhammad and Ahmad is included as one of the greatness of Allah SWT who has protected both these names from being used for anyone before his birth. Before he was born, none of the Arabs uses these names except after the news that a prophet with the name Muhammad will come. Hence, a small number of the Arabs named their children this with the hopes that they are the person meant. 
Imam Ibn ‘Asakir has stated in his book from a narration of Ibn ‘Abbas RA:
“When the Prophet PBUH was born, Abd al-Muttalib performed aqiqah for him by slaughtering a qibash and named him Muhammad. It was asked to him: “O Abu al-Harith, why did you give him the name Muhammad and not the name of his ancestors? He replied: “I wanted Allah SWT to praise him in the heavens and the people to praise him on earth.” 
To conclude, the Messenger PBUH is named Muhammad by his grandfather in the hopes that he’ll be praised by Allah SWT in the heavens and people on earth. The word Muhammad itself means a person who is praised and it is in the mubalaghah form which means the most praised. The name is suitable for he is the person who praises Allah SWT the most and is most praised over all the other prophets for his commendable characteristics.  Wallahu a’lam.